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 x 2 – 1 = 0 does not have a root lying between 0 and 2.

Question

Philoid · Accepted Answer

(i) 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 given statement p has to be proved false. For this purpose, it has to be proved that if q, then ~r.

To show this, angles of a triangle are required such that none of them is an obtuse angle.

It is known that the sum of all angles of a triangle is 180°.

Therefore, if all the three angles are equal, then each of them is of measure 60°, which is not an obtuse angle.

In an equilateral triangle, the measure of all angles is equal. However, the triangle is not an obtuse – angled triangle.

Thus, it can be concluded that given statement p is false.

(ii) Putting x = 1 in equation

x² – 1 = (1)² – 1 = 1 – 1 = 0

Hence x = 1 be the root of x² – 1 = 0

& x is lying between 0 & 2

Hence the given statement is not true.

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.

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.