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GATE | GATE-CS-2005 | Question 41

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What is the first order predicate calculus statement equivalent to the following? Every teacher is liked by some student (A) ∀(x) [teacher (x) → ∃ (y) [student (y) → likes (y, x)]] (B) ∀ (x) [teacher (x) → ∃ (y) [student (y) ^ likes (y, x)]] (C) ∃ (y) ∀ (x) [teacher (x) → [student (y) ^ likes (y, x)]] (D) ∀ (x) [teacher (x) ^ ∃ (y) [student (y) → likes (y, x)]]

Answer: (B)

Explanation: Answer is B] Statement : If X is a teacher then there exists some Y who is a student and likes X. A] Statement : If X is a teacher, then there exists a Y such that if Y is a student, then Y likes X. C] Statement : There exist a student who likes all teachers. D] Statement : Everyone is a teacher and there exists a Y such that if Y is student then y likes X.

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Last Updated : 11 Oct, 2021
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