Question -
Answer -
(i) The given statement is of theform “if q then r”.
q: All theangles of a triangle are equal.
r: Thetriangle is an obtuse-angled triangle.
The given statement p hasto be proved false. For this purpose, it has to be proved that if q,then ∼r.
To show this, angles of atriangle are required such that none of them is an obtuse angle.
It is known that the sum of allangles 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, themeasure of all angles is equal. However, the triangle is not an obtuse-angledtriangle.
Thus, it can be concluded thatthe given statement p is false.
(ii) The given statement is asfollows.
q: Theequation x2 – 1 = 0 does not have a root lyingbetween 0 and 2.
This statement has to be provedfalse. 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 isfalse.