By giving a counterexample,show that the following statement is not true.
$p:$ If all the angles of a triangle are equal,then the triangle is an obtuse-angled triangle.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The given statement is of the form 'if $q$ then $r$'.
$q:$ All the angles of a triangle are equal.
$r:$ The triangle is an obtuse-angled triangle.
The statement $p$ is false if we can find a case where $q$ is true but $r$ is false.
In an equilateral triangle,all three angles are equal to $60^{\circ}$.
Since $60^{\circ} < 90^{\circ}$,an equilateral triangle is an acute-angled triangle,not an obtuse-angled triangle.
Thus,the statement $p$ is false because we have found a counterexample (the equilateral triangle) where the premise is true but the conclusion is false.

Explore More

Similar Questions

The logical statement $[\sim(\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to

The statement pattern $[p \wedge (q \vee r)] \vee [\sim r \wedge \sim q \wedge p]$ is equivalent to

The dual of $(x \vee y) \wedge (x \vee 1) = x \vee (x \wedge y) \vee y$ is

Which of the following is logically equivalent to $(p \wedge q)$?

Simplify the following switching circuit and find the corresponding Boolean expression.

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