Find the component statements of the following and check whether they are true or not.
$\sqrt{2}$ is a rational number or an irrational number.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The component statements are:
$p: \sqrt{2}$ is a rational number.
$q: \sqrt{2}$ is an irrational number.
The first statement $p$ is false,as $\sqrt{2}$ cannot be expressed in the form $\frac{p}{q}$ where $p, q$ are integers and $q \neq 0$.
The second statement $q$ is true.
Since the connecting word is 'or',the compound statement is true if at least one of the component statements is true. Therefore,the compound statement is true.

Explore More

Similar Questions

Consider the following statements.
$p: \text{If } 3^4 > 4^3, \text{then } 3^3 > 4^1$
$q: \text{The roots of the equation } x^2 - 2x + 2 = 0 \text{ are real if and only if Mumbai is in Maharashtra.}$
$r: \text{Statement } p \text{ is true or statement } q \text{ is false.}$
Which of the following has truth value $T$ (true)?

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

Which of the following is the inverse of the proposition: "If a number is a prime then it is odd."

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

The dual of the statement $[p \vee (\sim q)] \wedge (\sim p)$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo