Negation of the statement: $\sqrt{5}$ is an integer or 5 is irrational' is:

(C) $\sqrt{5}$ is not an integer and 5 is not irrational

(A) $\sqrt{5}$ is an integer and 5 is irrational

(B) $\sqrt{5}$ is not an integer or 5 is not irrational

(D) $\sqrt{5}$ is irrational or 5 is an integer

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Mathematical Reasoning *

Negation of the statement:

5

is an integer or 5 is irrational' is:

Answer: (C)

The negation of 'p or q' is 'not p and not q'. Taking

p

to be the claim that

5

is an integer and

q

the claim that

5

is irrational, the negation reads that

5

is not an integer and

5

is not irrational.

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option