GATE | Sudo GATE 2020 Mock II (10 January 2019) | Question 22

Let C(x) denote “x is a cat”, R(x) denote “x is a rat” and P(x,y) denote “x chases y”.
Which of the following statements denotes “some cats chases all rats” ?
(A) ∃x[C(x)→ ∀y(R(y)→P(x,y)]
(B) ∃x[C(x)∧ ∀y(R(y)→P(x,y)]
(C) ∃x[C(x)∧ ∀y(R(y)∧P(x,y)]
(D) ∃x[C(x)∧ ∀y(R(x)→P(x,y)]

Answer: (B)

Explanation: There is something that is a cat and for any other thing, if that thing is a rat, then the cat chases it.

So it will be written as ∃x[C(x)∧ ∀y(R(y)→P(x,y)].

Option (B) is correct.

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