By giving a counter example, show that the following statements are not true
(i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle
(ii) q: The equation x² - 1 = 0 does not have a root lying between 0 and 2

Solution:

(i) The given statement is of the form ‘if r then s’ where

r: All the angles of a triangle are equal.

s: The triangle is an obtuse-angled triangle.

To prove the given statement p to be false, it has to be proved that "if r then not s".

So let us assume that r is true. Then all the angles of a triangle are equal.

We know that the sum of all angles of a triangle is 180° .

Then each angle of the triangle is 180°/3 = 60°. It means none of the angles is obtuse.

Hence the triangle is NOT an obtuse-angled triangle (in fact, it is an equilateral triangle).

So we proved that s is not true.

Thus, p is false.

(ii) Let us solve the equation x² - 1 = 0.

⇒ x² = 1

⇒ x = ± 1

⇒ x = 1 (or) x = -1.

Among these, the root x = 1, lies between 0 and 2.

Thus, the given statement is not true

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.5 Question 4

By giving a counter example, show that the following statements are not true. (i) p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle. (ii) q: The equation x² - 1 = 0 does not have a root lying between 0 and 2.

Summary:

(i) The statement "p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle." is proved to be not true
(ii) The statement "q: The equation x² - 1 = 0 does not have a root lying between 0 and 2." is proved to be not true