Question 9439 – Propositional-Logic

What is the first order predicate calculus statement equivalent to the following?

   Every teacher is liked by some student

Correct Answer: B

Question 27 Explanation:

Option A: If x is a teacher, then there exist a y such that if y is a student , then y likes x.
Option B: If x is a teacher, then there exists some y, who is a student and like x. (✔️)
Option C: There exists a student who likes all teachers.
Option D: If x is a teacher and then there exists some y, if y is a student then y likes x.

∀(x) [teacher(x) → ∃ (y) [student(y) → likes (y, x)]]

∀(x) [teacher(x) → ∃ (y) [student(y) ∧ likes (y, x)]]

∃(y) ∀(x) [teacher(x) → [student(y) ∧ likes (y, x)]]

∀(x) [teacher(x) ∧ ∃ (y)[student(y) → likes (y, x)]]

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