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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))]

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))] Correct Answer Only bears eat fish

Concept:

∀x states that all the times when x is a fish, if x is eaten by something, that something is sure to be a bear. Simplifying this, it can be said that if anyone eats fish then that anyone has to be bear. Only bears eat fish.

Explanation:

Option 1: Every fish is eaten by some bear

∀x(F(x)⇒∃y(B(y)∧E(y, x))) which means that for all x, if x is a fish, then there is a y such that y is a bear and y eats x. That is, every fish going to be eater and that too by some bear only.

Option_2: Bears eat only fish

∀x(B(x)⇒∀y(E(x, y)−>F(y)) which means that for every x, if x is a bear, then for all y, if x eats y, then y is a fish. That is, if bears eat anything, that anything has to be a fish.

Option 3: Every bear eats fish

∀x(B(x)⇒∃y(F(y)∧E(x, y)) which states that for all x, if x is a bear, then there is a y such that, y is a fish and x eats y. That is, each and every bear eats fish and fish only.

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