Q41

MCQ2 marks, −0.5

What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student"

(A)

$∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$

(B)

$∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) ∧ \text{likes}\left(y,x\right)\right]\right]$

(C)

$∃(y) ∀(x)\left[\text{teacher}\left(x\right) → \left[\text{student}\left(y\right) ∧ \text{likes}\left(y,x\right)\right]\right]$

(D)

$∀(x)\left[\text{teacher}\left(x\right) ∧ ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$

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