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

Answer: (D)

$p=\sqrt{5}$ is an integer.
$q : 5$ is irrational
$\sim\left(p\,\vee\,q\right)\equiv\sim p\,\wedge\,\sim q$
$=\sqrt{5}$ is not an integer and 5 is not irrational.