# 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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