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# GATE | GATE-CS-2005 | Question 41

• Last Updated : 28 Jun, 2021

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)]]

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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