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.

Explanation for the correct option:

Finding the negation of the given statement:

Given Statement: ′$\sqrt{5}$is an integer or $5$ is irrational′

Let $p:\sqrt{5}$ is an integer

and $q:5$is irrational

The statement is $p\vee q$

$~p:\sqrt{5}$ is not an integer.

$~q:5$ is not irrational

Therefore the negation of the statement is $~(p\vee q)=~p\wedge ~q$

$\sqrt{5}$ is not an integer and $5$ is not irrational.

Hence the correct option is (D).