p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle
(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.
