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

Explanation

(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 obtuse-angled
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 obtuse-angled.
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