GATE | GATE-CS-2002 | Question 8
“If X, then Y unless Z” is represented by which of the following formulae in propositional logic?
(“¬” is negation “^” is conjunction, and “→” is implication)
(A) (X ^ ¬ Z) → Y
(B) (X ^ Y) → ¬ Z
(C) (X → (Y ^ ¬ Z)
(D) (X → Y(^ ¬ Z)
Explanation: The statement “If X then Y unless Z” means, if Z doesn’t occur, X implies Y i.e. ¬Z→(X→Y), which is equivalent to Z ∨ (X→Y)
(since P→Q ≡ ¬P ∨ Q), which is then equivalent to Z ∨ (¬X ∨ Y). Now we can look into options which one matches with this.
So option (a) is (X∧¬Z)→Y = ¬( (X∧¬Z) ) ∨ Y = (¬X∨Z) ∨ Y, which matches our expression. So option (A) is correct.
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