Kanazawa University Graduate School of Law
Jurisprudence, Final examination
26 July 2024, Hidehiko Adachi

Note: In case of any discrepancies between the English and Japanese versions, the Japanese version shall prevail. The English version is provided forreference purposes only.
1. Explain, using truth tables, whether the following reasonings are valid(logically correct). If not, provide counterexamples.
(a) ¬A therefore A → B(b) A → B, B therefore A

2. Explain, using tableaux (truth trees), whether the following reasonings
are valid. If not, provide counterexamples.
(a) A ∨ B, A → C, B → C therefore C(b) A therefore A → B

3. Explain, using a tableau, whether the following logical formula a tautology.
((A → B) → A) → A
4. Translate the sentences (a)-(d) into
• logical formulae containing the all quantiﬁers and ‘if’, and• logical formulae containing the existential quantiﬁers and ‘and’and• write Venn Diagrams.
Let the predicate ‘S’ represent ‘is a law school student’ and the predicate ‘J’ represent ‘is studying jurisprudence’.
(a) Every law school students are studying Jurisprudence.
(b) No law school students is studying Jurisprudence.
(c) There is someone who is a law school student and isn’t studying
Jirisprudence.
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(d) There is someone who is a law school student and studying Jirisprudence.

5. Are the following statements correct? Write a ○ if it is correct and a× if it is not. If ×, explain what is wrong and how it can be corrected.
(a) A proposition is the content of a sentence that has a truth value.
(b) If two logical formulae A and B are logical equivalent, then thetruth values of A and B are the same in any case.
(c) The inference ‘a must compensate b for the damage and is permitted not to compensate b for it’ and therefore ‘b must be grateful
to a’ is logically incorrect.
(d) Inference (Reasoning) that has no counterexample and in which
all premises are true is called sound inference.
(e) ⊨ (therefore) is a logical connective of propositional logic.
(f) The fact that a set of logical formulae is consistent means that, inany case, all the logical formulae in the set will be true.
(g) If the inference ‘A, therefore B’ is valid, then the proposition ‘A
then B’ is a tautology.
(h) Permission for omission (inaction) implies prohibition of action.
(i) The impossible is not obligatory.
(j) The fact that an action is obligatory and its inaction is also obligatory is called non-freedom.
(k) If it is obligatory not to smoke, it is also obligatory to pay a million
yen if you smoke.
(l) In countries where freedom of speech is not guaranteed (assumingthat freedom of speech is explicitly denied by statute or case law),citizens are prohibited from speaking out against the government.
(m) A non-consistent world is not a possible world.
(n) In a world where murder is prohibited, no one commits murder.
(o) ‘Whoever kills a person shall be liable to a custodial sentence of
not less than ﬁve years’ is an unconditional general norm.
(p) According to Gustav Radbruch, the law is the possibility of morals,
and for that very reason it is also the possibility of the immoral.
2(q) In countries where there is no freedom to believe in a religion, thestate has the right to require its citizens to believe in a religion,
as well as the right to require them not to believe in a religion.
(r) Many of the obligations established by statutory provisions are
non-defeasible obligations.
(s) In the absence of a law prohibiting not learning, it is legally permissible not learning.
(t) Property rights are freedom-rights of all persons over a certainperson.
(u) Radbruch named the norms that conferred on the ﬁrst constitution
makers in history the power to set up their constitutions as thebasic norm (Grundnorm).
(v) Setting out the rights of citizens in a constitution and prohibiting
them from being signiﬁcantly changed or abolished is known asinstitutional guarantees.
(w) The Constitution gives the courts the competence to judge cases,
but does not oblige them to exercise this competence.
(x) A norm that sets out the best situation or action, but does not
specify what should be done if that situation or action is notrealised, is called a principle.
(y) Arguments based on the legislator’s will are arguments based on
the actual will of the current legislator.
(z) Gaps in the law are exceptional in private law.

6. Fill in the blanks in the following sentences.
(a) A formula that is always true regardless of the truth value combination of atomic formulae is called (1), a formulathat is always false is called (2), and a formula thatcan be both true and false is called (3).
(b) Order (duty to act), prohibition and freedom are in a relationship of (1) with each other, non-freedom, permission
to act and permission to omit are in a relationship of (2) with each other, order（3） permission to act andnon-freedom, prohibition（3）permission to omit andnon-freedom, freedom （3） permission to act andpermission to omit
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7. Explain the following words and phrases.
(a) freedom(b) competence (power)(c) commutative justice(d) contingent interpretation of law(e) contra legem4