Given that B(a) means “a is a bear” F(a) means “a is a fish” and E(a, b) means…

2020

Given that

B(a) means “a is a bear”
F(a) means “a is a fish” and
E(a, b) means “a eats b” 

Then what is the best meaning of

∀x[F(x) ⇒ ∀y(E(y, x) ⇒ B(y))] 

Answer: D. Only bears eat fishThe formula ∀x[F(x) ⇒ ∀y(E(y, x) ⇒ B(y))] translates to: For any entity x, if x is a fish, then for any entity y, if y eats x, y must be a bear. This means…

  1. A.

    Every fish is eaten by some bear

  2. B.

    Bears eat only fish

  3. C.

    Every bear eats fish

  4. D.

    Only bears eat fish

Attempted by 85 students.

Show answer & explanation

Correct answer: D

The formula ∀x[F(x) ⇒ ∀y(E(y, x) ⇒ B(y))] translates to: For any entity x, if x is a fish, then for any entity y, if y eats x, y must be a bear. This means that anyone or anything eating a fish is necessarily a bear. Thus, the statement implies that only bears eat fish.

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