[
  {
    "id": 457260,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 401315,
    "position": 12,
    "question_name": "Question 12",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Using the translation in the previous question, draw a tree to check whether 'it's raining and I don't believe it's raining' is a contradiction in D4 (which is K with extendability and transitivity), an appropriate model for (rational) belief.</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 8272,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 3601,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 8141,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 1987,
        "text": "closed and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 457266,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 401317,
    "position": 13,
    "question_name": "Question 13",
    "question_type": "true_false_question",
    "question_text": "<p>If the correct logic for belief is D4, 'it's raining and I don't believe it' is a contradiction.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 5841
      },
      {
        "text": "False",
        "id": 5641
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 457289,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 401328,
    "position": 15,
    "question_name": "Question 15",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still using the same translations as before, draw a tree to check whether 'I believe both that it's raining and that I don't believe it's raining' is a contradiction in D4 (which is K with extendability and transitivity).</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 6493,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 1060,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 2068,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 4184,
        "text": "open and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 475742,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 418497,
    "position": 11,
    "question_name": "Question 11",
    "question_type": "matching_question",
    "question_text": "<p>Match the forms below with the corresponding English sentences, translating 'I believe that' using the square.</p>\n<p>(a) <img class=\"equation_image\" title=\"p \\wedge \\neg \\square p\" src=\"https://canvas.nus.edu.sg/equation_images/p%2520%255Cwedge%2520%255Cneg%2520%255Csquare%2520p?scale=1\" alt=\"LaTeX: p \\wedge \\neg \\square p\" data-equation-content=\"p \\wedge \\neg \\square p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>p</mi>\n  <mo>&amp;#x2227;<!-- \u2227 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>(b) <img class=\"equation_image\" title=\"p \\wedge \\square \\neg p\" src=\"https://canvas.nus.edu.sg/equation_images/p%2520%255Cwedge%2520%255Csquare%2520%255Cneg%2520p?scale=1\" alt=\"LaTeX: p \\wedge \\square \\neg p\" data-equation-content=\"p \\wedge \\square \\neg p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>p</mi>\n  <mo>&amp;#x2227;<!-- \u2227 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>(c) <img class=\"equation_image\" title=\"\\square (p \\wedge \\neg \\square p)\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare%2520(p%2520%255Cwedge%2520%255Cneg%2520%255Csquare%2520p)?scale=1\" alt=\"LaTeX: \\square (p \\wedge \\neg \\square p)\" data-equation-content=\"\\square (p \\wedge \\neg \\square p)\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2227;<!-- \u2227 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n</math>\"></p>\n<p>(d) <img class=\"equation_image\" title=\"\\square (p \\wedge \\square \\neg p)\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare%2520(p%2520%255Cwedge%2520%255Csquare%2520%255Cneg%2520p)?scale=1\" alt=\"LaTeX: \\square (p \\wedge \\square \\neg p)\" data-equation-content=\"\\square (p \\wedge \\square \\neg p)\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2227;<!-- \u2227 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n</math>\"></p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 3301,
        "text": "(a)"
      },
      {
        "id": 6355,
        "text": "(b)"
      },
      {
        "id": 2340,
        "text": "(c)"
      },
      {
        "id": 6286,
        "text": "(d)"
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": [
      {
        "text": "I believe both that it's raining and that I believe it's not raining",
        "match_id": 7798
      },
      {
        "text": "I believe both that it's raining and that I don't believe it's raining",
        "match_id": 2085
      },
      {
        "text": "It's raining and I believe it's not raining",
        "match_id": 8793
      },
      {
        "text": "It's raining and I don't believe it's raining",
        "match_id": 3707
      }
    ],
    "flagged": false,
    "answer": [
      {
        "answer_id": "3301",
        "match_id": null
      },
      {
        "answer_id": "6355",
        "match_id": null
      },
      {
        "answer_id": "2340",
        "match_id": null
      },
      {
        "answer_id": "6286",
        "match_id": null
      }
    ]
  },
  {
    "id": 478789,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420281,
    "position": 1,
    "question_name": "Question 1",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Consider the argument: 'If God exists, then necessarily God exists. Possibly, God exists. Therefore, God exists'.</p>\n<p>Suppose the form of this argument is: <img class=\"equation_image\" title=\"p \\supset \\square p, \\diamond p \\therefore p\" src=\"https://canvas.nus.edu.sg/equation_images/p%2520%255Csupset%2520%255Csquare%2520p%252C%2520%255Cdiamond%2520p%2520%255Ctherefore%2520p?scale=1\" alt=\"LaTeX: p \\supset \\square p, \\diamond p \\therefore p\" data-equation-content=\"p \\supset \\square p, \\diamond p \\therefore p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi>p</mi>\n</math>\"></p>\n<p>Then draw a tree to check whether this argument is valid in S5 (for which see the textbook, section 3.5 pp. 45-6). The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 2734,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 4920,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 1839,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 1147,
        "text": "closed and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478790,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420282,
    "position": 2,
    "question_name": "Question 2",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Now consider the argument: 'If God exists, then necessarily God exists. Possibly, God does not exist. Therefore, God does not exist'.</p>\n<p>Suppose the form of this argument is: <img class=\"equation_image\" title=\"p \\supset \\square p, \\diamond \\neg p \\therefore \\neg p\" src=\"https://canvas.nus.edu.sg/equation_images/p%2520%255Csupset%2520%255Csquare%2520p%252C%2520%255Cdiamond%2520%255Cneg%2520p%2520%255Ctherefore%2520%255Cneg%2520p?scale=1\" alt=\"LaTeX: p \\supset \\square p, \\diamond \\neg p \\therefore \\neg p\" data-equation-content=\"p \\supset \\square p, \\diamond \\neg p \\therefore \\neg p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>Then draw a tree to check whether this argument is valid in K, the weakest normal modal logic (see the textbook, section 2.4 pp. 24-8 for the rules). The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 2142,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 4767,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 920,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 5529,
        "text": "open and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478794,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420283,
    "position": 3,
    "question_name": "Question 3",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Let's suppose the correct modal logic for necessity and possibility is at least as strong as K but no stronger than S5, and that the translations in the previous two questions are correct. It follows that:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 3829,
        "text": "both arguments are valid",
        "html": ""
      },
      {
        "id": 6386,
        "text": "the argument for atheism is valid but the argument for theism is not",
        "html": ""
      },
      {
        "id": 4790,
        "text": "both arguments are invalid",
        "html": ""
      },
      {
        "id": 3630,
        "text": "the argument for theism is valid but the argument for atheism is not",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478807,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420287,
    "position": 4,
    "question_name": "Question 4",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Reconsider the argument: 'If God exists, then necessarily God exists. Possibly, God exists. Therefore, God exists'.</p>\n<p>But now suppose the form of this argument is: <img class=\"equation_image\" title=\"\\square( p \\supset \\square p), \\diamond p \\therefore p\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare(%2520p%2520%255Csupset%2520%255Csquare%2520p)%252C%2520%255Cdiamond%2520p%2520%255Ctherefore%2520p?scale=1\" alt=\"LaTeX: \\square( p \\supset \\square p), \\diamond p \\therefore p\" data-equation-content=\"\\square( p \\supset \\square p), \\diamond p \\therefore p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi>p</mi>\n</math>\"></p>\n<p>(In other words, suppose the conditional in the first premise is strict. For strict conditionals, see the textbook, section 4.5, p. 72.)</p>\n<p>Then draw a tree to check whether this argument is valid in S4 (which is K with the addition of reflexivity and transitivity). The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 9196,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 517,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 448,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 3214,
        "text": "closed and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478808,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420288,
    "position": 5,
    "question_name": "Question 5",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still considering the argument: 'If God exists, then necessarily God exists. Possibly, God exists. Therefore, God exists'.</p>\n<p>And continuing to suppose the form of this argument is: <img class=\"equation_image\" title=\"\\square( p \\supset \\square p), \\diamond p \\therefore p\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare(%2520p%2520%255Csupset%2520%255Csquare%2520p)%252C%2520%255Cdiamond%2520p%2520%255Ctherefore%2520p?scale=1\" alt=\"LaTeX: \\square( p \\supset \\square p), \\diamond p \\therefore p\" data-equation-content=\"\\square( p \\supset \\square p), \\diamond p \\therefore p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi>p</mi>\n</math>\"></p>\n<p><span style=\"color: var(--ic-brand-font-color-dark); font-family: inherit; font-size: 1rem;\">Draw a tree to check whether this argument is valid in S5 (which is K with the addition of reflexivity, symmetry, and transitivity). The completed tree is:</span></p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 6821,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 3091,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 6359,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 3074,
        "text": "open and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478811,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420291,
    "position": 6,
    "question_name": "Question 6",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still considering the argument: 'If God exists, then necessarily God exists. Possibly, God exists. Therefore, God exists'.</p>\n<p>And continuing to suppose the form of this argument is: <img class=\"equation_image\" title=\"\\square( p \\supset \\square p), \\diamond p \\therefore p\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare(%2520p%2520%255Csupset%2520%255Csquare%2520p)%252C%2520%255Cdiamond%2520p%2520%255Ctherefore%2520p?scale=1\" alt=\"LaTeX: \\square( p \\supset \\square p), \\diamond p \\therefore p\" data-equation-content=\"\\square( p \\supset \\square p), \\diamond p \\therefore p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi>p</mi>\n</math>\"></p>\n<p>Which modal logic should be preferred by an atheist who accepts the premises but rejects the conclusion of this argument?</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 5087,
        "text": "S4",
        "html": ""
      },
      {
        "id": 6276,
        "text": "S5",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478814,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420292,
    "position": 7,
    "question_name": "Question 7",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Now reconsider the argument: 'If God exists, then necessarily God exists. Possibly, God does not exist. Therefore, God does not exist'.</p>\n<p>But now suppose the form of this argument is: <img class=\"equation_image\" title=\"\\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare(%2520p%2520%255Csupset%2520%255Csquare%2520p)%252C%2520%255Cdiamond%2520%255Cneg%2520p%2520%255Ctherefore%2520%255Cneg%2520p?scale=1\" alt=\"LaTeX: \\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" data-equation-content=\"\\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>(In other words, suppose the conditional in the first premise is strict.)</p>\n<p>Then draw a tree to check whether this argument is valid in K. The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 8744,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 9531,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 3948,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 979,
        "text": "open and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478815,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420293,
    "position": 8,
    "question_name": "Question 8",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still considering the argument: 'If God exists, then necessarily God exists. Possibly, God does not exist. Therefore, God does not exist'.</p>\n<p>And continuing to suppose the form of this argument is: <img class=\"equation_image\" title=\"\\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare(%2520p%2520%255Csupset%2520%255Csquare%2520p)%252C%2520%255Cdiamond%2520%255Cneg%2520p%2520%255Ctherefore%2520%255Cneg%2520p?scale=1\" alt=\"LaTeX: \\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" data-equation-content=\"\\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>Draw a tree to check whether this argument is valid in T (which is K with reflexivity). The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 1455,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 6968,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 4694,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 8872,
        "text": "closed and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478817,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420294,
    "position": 9,
    "question_name": "Question 9",
    "question_type": "true_false_question",
    "question_text": "<p>If the argument 'If God exists, then necessarily God exists. Possibly, God does not exist. Therefore, God does not exist' has the form: <img class=\"equation_image\" title=\"\\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare(%2520p%2520%255Csupset%2520%255Csquare%2520p)%252C%2520%255Cdiamond%2520%255Cneg%2520p%2520%255Ctherefore%2520%255Cneg%2520p?scale=1\" alt=\"LaTeX: \\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" data-equation-content=\"\\square( p \\supset \\square p), \\diamond \\neg p \\therefore \\neg p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2283;<!-- \u2283 --></mo>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n  <mo>,</mo>\n  <mo>&amp;#x22C4;<!-- \u22c4 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n  <mo>&amp;#x2234;<!-- \u2234 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>then it is valid in T and therefore S5.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 7806
      },
      {
        "text": "False",
        "id": 4919
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478820,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420295,
    "position": 10,
    "question_name": "Question 10",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Finally, consider the two arguments together:</p>\n<p>'If God exists, then necessarily God exists. Possibly, God exists. Therefore, God exists.'</p>\n<p>'If God exists, then necessarily God exists. Possibly, God does not exist. Therefore, God does not exist.'</p>\n<p>Supposing that the right modal logic for assessing these arguments is S5, we conclude from the previous questions that:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 8091,
        "text": "both arguments are sound, but one is invalid",
        "html": ""
      },
      {
        "id": 2270,
        "text": "both arguments are invalid and unsound",
        "html": ""
      },
      {
        "id": 9219,
        "text": "both arguments are sound and valid",
        "html": ""
      },
      {
        "id": 5173,
        "text": "both arguments are valid, but one is unsound",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478828,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420297,
    "position": 16,
    "question_name": "Question 16",
    "question_type": "true_false_question",
    "question_text": "<p>If the correct logic for belief is D4, 'I believe both that it's raining and that I don't believe it's raining' is a contradiction.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 7204
      },
      {
        "text": "False",
        "id": 5642
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478854,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420323,
    "position": 14,
    "question_name": "Question 14",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still using the same translations as before, draw a tree to check whether 'I believe both that it's raining and that I don't believe it's raining' is a contradiction in D (which is K with extendability).</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 7086,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 7882,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 7654,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 1746,
        "text": "open and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478883,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420349,
    "position": 17,
    "question_name": "Question 17",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Suppose the correct logic for belief is D4. Then the fact that 'it's raining and I don't believe it' is absurd may be explained because:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 8208,
        "text": "it's possible, and it's possible to believe",
        "html": ""
      },
      {
        "id": 5456,
        "text": "it's impossible, and it's impossible to believe",
        "html": ""
      },
      {
        "id": 9314,
        "text": "it's possible, but it is impossible to believe",
        "html": ""
      },
      {
        "id": 5530,
        "text": "it's impossible, but it's possible to believe",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478885,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420350,
    "position": 18,
    "question_name": "Question 18",
    "question_type": "multiple_choice_question",
    "question_text": "<p>The solution to Moore's paradox we reached in the last question is due to Jaakko Hintikka (in his book \"Knowledge and Belief\").</p>\n<p>Because Hintikka's solution requires the logic of belief to be D4 and not just D, he is committed to the thesis that:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 1685,
        "text": "if p, then I believe p",
        "html": ""
      },
      {
        "id": 6068,
        "text": "If I believe p, then p",
        "html": ""
      },
      {
        "id": 7900,
        "text": "If I believe I believe p, then I believe p",
        "html": ""
      },
      {
        "id": 1044,
        "text": "If I believe p, I believe that I believe that p",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478889,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420351,
    "position": 21,
    "question_name": "Question 21",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still using the same translations as before, draw a tree to check whether 'I believe both that it's raining and that I believe it's not raining' is a contradiction in D4.</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 8835,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 2703,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 9206,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 7128,
        "text": "closed and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478892,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420352,
    "position": 19,
    "question_name": "Question 19",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still using the same translations as before, draw a tree to check whether 'it's raining and I believe it's not raining' is a contradiction in D4.</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 2118,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 5018,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 3293,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 6928,
        "text": "closed and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478893,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420353,
    "position": 20,
    "question_name": "Question 20",
    "question_type": "true_false_question",
    "question_text": "<p>If D4 is the correct logic for belief, then 'it's raining and I believe it's not raining' is a contradiction.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 5990
      },
      {
        "text": "False",
        "id": 648
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478894,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420354,
    "position": 22,
    "question_name": "Question 22",
    "question_type": "true_false_question",
    "question_text": "<p>If D4 is the correct logic for belief, then 'I believe both that it's raining and that I believe it's not raining' is a contradiction.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 7981
      },
      {
        "text": "False",
        "id": 4302
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478897,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420355,
    "position": 23,
    "question_name": "Question 23",
    "question_type": "true_false_question",
    "question_text": "<p>If D4 is the correct logic for belief, Hintikka can use this to explain the absurdity of 'it's raining and I believe it's not raining' as well as 'it's raining and I don't believe it's raining'.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 6463
      },
      {
        "text": "False",
        "id": 1841
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478900,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420357,
    "position": 24,
    "question_name": "Question 24",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Consider 'it's raining and I don't know it's raining', and suppose it also has the form: <img class=\"equation_image\" title=\"p \\wedge \\neg \\square p\" src=\"https://canvas.nus.edu.sg/equation_images/p%2520%255Cwedge%2520%255Cneg%2520%255Csquare%2520p?scale=1\" alt=\"LaTeX: p \\wedge \\neg \\square p\" data-equation-content=\"p \\wedge \\neg \\square p\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>p</mi>\n  <mo>&amp;#x2227;<!-- \u2227 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n</math>\"></p>\n<p>where we now use the box to translate 'I know that'. Draw a tree to check whether 'it's raining and I don't know it's raining' is a contradiction in S4 (which is K with reflexivity and transitivity), an appropriate logic for modelling knowledge.</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 6751,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 7907,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 9336,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 5912,
        "text": "closed and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478901,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420358,
    "position": 25,
    "question_name": "Question 25",
    "question_type": "true_false_question",
    "question_text": "<p>If the correct logic for knowledge is S4, 'it's raining and I don't know it's raining' is a contradiction.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 1749
      },
      {
        "text": "False",
        "id": 37
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478903,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420359,
    "position": 26,
    "question_name": "Question 26",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Now consider 'I know both that it's raining and that I don't know it's raining', and suppose it has the form:<span> <img class=\"equation_image\" title=\"\\square (p \\wedge \\neg \\square p)\" src=\"https://canvas.nus.edu.sg/equation_images/%255Csquare%2520(p%2520%255Cwedge%2520%255Cneg%2520%255Csquare%2520p)?scale=1\" alt=\"LaTeX: \\square (p \\wedge \\neg \\square p)\" data-equation-content=\"\\square (p \\wedge \\neg \\square p)\" data-ignore-a11y-check=\"\" x-canvaslms-safe-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mo stretchy=&quot;false&quot;>(</mo>\n  <mi>p</mi>\n  <mo>&amp;#x2227;<!-- \u2227 --></mo>\n  <mi mathvariant=&quot;normal&quot;>&amp;#x00AC;<!-- \u00ac --></mi>\n  <mi>&amp;#x25FB;<!-- \u25fb --></mi>\n  <mi>p</mi>\n  <mo stretchy=&quot;false&quot;>)</mo>\n</math>\"></span></p>\n<p>Draw a tree to check whether 'I know both that it's raining and that I don't know it's raining' is a contradiction in S4.</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 9360,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 4768,
        "text": "closed and infinite",
        "html": ""
      },
      {
        "id": 6838,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 2039,
        "text": "closed and finite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478904,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420360,
    "position": 27,
    "question_name": "Question 27",
    "question_type": "true_false_question",
    "question_text": "<p>If the correct logic for knowledge is S4, 'I know both that it's raining and that I don't know it's raining' is a contradiction.</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "text": "True",
        "id": 7743
      },
      {
        "text": "False",
        "id": 372
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478908,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420361,
    "position": 28,
    "question_name": "Question 28",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Suppose the correct logic for knowledge is S4. Then the fact that 'it's raining and I don't know it is raining' is absurd may be explained because:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 1436,
        "text": "it's possible, and it's possible to know it",
        "html": ""
      },
      {
        "id": 2354,
        "text": "it's possible, but it's impossible to know it",
        "html": ""
      },
      {
        "id": 8894,
        "text": "it's impossible, but it's possible to know it",
        "html": ""
      },
      {
        "id": 540,
        "text": "it's impossible, and it's impossible to know it",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478911,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420362,
    "position": 29,
    "question_name": "Question 29",
    "question_type": "multiple_choice_question",
    "question_text": "<p>Still using the same translations as before, draw a tree to check whether 'I know both that it's raining and that I don't know it's raining' is a contradiction in T (which is K with reflexivity).</p>\n<p>The completed tree is:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 9000,
        "text": "open and infinite",
        "html": ""
      },
      {
        "id": 7394,
        "text": "open and finite",
        "html": ""
      },
      {
        "id": 182,
        "text": "closed and finite",
        "html": ""
      },
      {
        "id": 814,
        "text": "closed and infinite",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  },
  {
    "id": 478912,
    "quiz_id": 46047,
    "quiz_group_id": null,
    "assessment_question_id": 420363,
    "position": 30,
    "question_name": "Question 30",
    "question_type": "multiple_choice_question",
    "question_text": "<p>The solution to Moore's paradox in knowledge we reached in the last question was also advocated by Hintikka.</p>\n<p>Given your answers to the previous questions about whether 'I know both that it's raining and that I don't know it's raining' is a contradiction in&nbsp; T and S4, this part of Hintikka's solution is only committed to the principle that:</p><script src=\"https://instructure-uploads-apse1.s3.ap-southeast-1.amazonaws.com/account_214500000000000001/attachments/18442/BlueCanvasMobileConfig.js\"></script>",
    "answers": [
      {
        "id": 8389,
        "text": "if you know p, then you know that you know that p",
        "html": ""
      },
      {
        "id": 3880,
        "text": "if p, then you know that p",
        "html": ""
      },
      {
        "id": 6515,
        "text": "if you don't know that p, then not p",
        "html": ""
      },
      {
        "id": 2572,
        "text": "if you know that p, then p",
        "html": ""
      }
    ],
    "variables": null,
    "formulas": null,
    "answer_tolerance": null,
    "formula_decimal_places": null,
    "matches": null,
    "flagged": false,
    "answer": null
  }
]

Answer all the questions defined in the JSON format.