(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 the given statement p is false.

(ii) The given statement is as follows.q:

The equation x² – 1 = 0 does not have a root lying between 0 and 2.

This statement has to be proved false. To show this, a counter example is required.

Consider x² – 1 = 0 

x² = 1 

x = ± 1

One root of the equation x² – 1 = 0, i.e. the root x = 1, lies between 0 and 2.

Thus, the given statement is false.