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.