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GATE | GATE-CS-2002 | Question 8

Last Updated : 18 Jun, 2021
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\”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)



Answer: (A)

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. Source: http://www.cse.iitd.ac.in/~mittal/gate/gate_math_2002.html


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