Topic: Diverse Conceptual Associations
help me with this question:

2 Crystal clear (Logic problem)
Although you are looking for it everywhere, you cannot find your true love. A bit desperate, you
decide to see Madame Irma, the most famous (and serious) fortune teller of the city. On the entrance,
you see a sign stating: Everything that I say must be proved to be believed. More perplexed than ever,
you still go inside. After glaring at you for some time, she looks into her crystal ball, which has a
strange glow, and says in a mysterious voice:
• You have a dog.
• The person you are looking for buys carrots by the bushel.
• Anyone who owns a rabbit hates anything that chases any rabbit.
• Every dog chases some rabbit.
• Anyone who buys carrots by the bushel owns either a rabbit or a grocery store.
• Someone who hates something owned by another person will not date that person.
The sentences you just heard reminds you of a person: Robin. But before you leave, she challenges
you with a conclusion:
• If the person you are looking for does not own a grocery store, she will not date you.
Remembering the sentence at the entrance, you realise that what she has told you is true only if you
can prove her challenging conclusion. Since you do not want any awkward situation, you decide to
provide proof of her conclusion before going to see Robin.
1. Express Madame Irma’s six statements into First Order Logic (FOL). Note: You can use two
constants: YOU and ROBIN.
This question carries 10% of the mark for this coursework.
2. Translate the obtained expressions to Conjunctive Normal Forms (CNFs, Steps 1-6 of Lecture
9: Logic). Show and explain your work.
This question carries 10% of the mark for this coursework.
3. Transform Madame Irma’s conclusion into FOL, negate it and convert it to CNF (Steps 1-6 of
Lecture 9: Logic). Show and explain your work.
This question carries 10% of the mark for this coursework.
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4. Based on all the previously created clauses (you should have at least 7 depending on how you
split them), finalise the conversion to CNF (Steps 7-8 of Lecture 9: Logic) and provide proof by
resolution that Madame Irma is right that you should go to see Robin to declare your (logic)
love to her. Show and explain your work, and provide unifiers.
This question carries 20% of the mark for this coursework.
Note: Make sure to follow the order of steps for the CNF conversion as given in Lecture 9, and report
all the steps (state “nothing to do” for the steps where this is the case).