Skip to content
Related Articles
GATE | GATE-CS-2005 | Question 41
• Last Updated : 12 Sep, 2014

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.

Quiz of this Question

Attention reader! Don’t stop learning now. Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up