"If X, then Y unless Z" is represented by which of the following formulae in…
2002
"If X, then Y unless Z" is represented by which of the following formulae in propositional logic? (¬ denotes negation, ∧ denotes conjunction, and → denotes implication.)
- A.
(X ∧ ¬Z) → Y
- B.
(X ∧ Y) → ¬Z
- C.
X → (Y ∧ ¬Z)
- D.
(X → Y) ∧ ¬Z
Attempted by 19 students.
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Correct answer: A
The phrase "Y unless Z" means Y is required when Z is false. Therefore, "If X, then Y unless Z" means: if X is true and Z is false, then Y must be true. The antecedent is X ∧ ¬Z and the consequent is Y. Hence the formula is (X ∧ ¬Z) → Y.