Question

Negation of the statement $p:\frac{1}{2}$ is rational and $\sqrt{3}$ is irrational is

• A. $\frac{1}{2}$ is rational or $\sqrt{3}$ is irrational
• B. $\frac{1}{2}$ is not rational or $\sqrt{3}$ is not irrational
• C. $\frac{1}{2}$ is not rational or $\sqrt{3}$ is irrational
• D. $\frac{1}{2}$ is rational and $\sqrt{3}$ is irrational

Answer 1

The correct option is A $\frac{1}{2}$ is rational or $\sqrt{3}$ is irrational

We know that $\sim (p\wedge q)=\sim p\vee \sim q$

Thus, negation of given statement is $\frac{1}{2}$ is not rational or $\sqrt{3}$ is not irrational