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GATE | GATE-CS-2002 | Question 8
• Difficulty Level : Easy
• Last Updated : 29 Nov, 2014

“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. ¬\negZ\to(X\toY), which is equivalent to Z\vee(X\toY) (since P\toQ ≡ ¬\negP\veeQ), which is then equivalent to Z\vee(¬\negX\veeY). Now we can look into options which one matches with this.

So option (a) is (X¬\wedge\negZ)\toY = ¬\neg((X¬\wedge\negZ))\veeY = (¬\negX\veeZ)\veeY, which matches our expression. So option A is correct.

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