Question

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

• A. $\sqrt{5}$ is irrational or $5$ is an integer
• B. $\sqrt{5}$ is not an integer or $5$ is not irrational
• C. $\sqrt{5}$ is an integer and $5$ is irrational
• D. $\sqrt{5}$ is not an integer and $5$ is not irrational

Answer 1

The correct option is D $\sqrt{5}$ is not an integer and $5$ is not irrational

$p:\sqrt{5}$ is an integer
$q:5$ is an irrational number
Given statement : $p\vee$ q
Required negation statement : $\sim (p\vee q)=\sim p\wedge \sim q$
${}^{\prime }\sqrt{5}$ is not an integer and $5$ is not irrational'