ISRO | ISRO CS 2020 | Question 11

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))] 

(A) Every fish is eaten by some bear
(B) Bears eat only fish
(C) Every bear eats fish
(D) Only bears eat fish


Answer: (D)

Explanation: According to Predicates and Quantifiers,

• (A) Every fish is eaten by some bear :

  ∀x(F(x) ⇒ ∃y(B(y)∧E(y,x))) 

• (B) Bears eat only fish :

  ∀x(B(x) ⇒ ∀y(E(x,y)⇒F(y)) 

• (C) Every bear eats fish :

  ∀x(B(x) ⇒ ∃y(F(y)∧E(x,y)) 

• (D) Only bears eat fish :

  ∀x[F(x) ⇒ ∀y(E(y, x) ⇒ B(y))] 

  Which is equivalent to “For every x if x is a fish then if it is eaten by y then that y is only bear.”

Option (D) is correct.

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