By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.
By giving a counter-example, show that the statement is false : p : If n is an odd positive integer, then n is prime.
Consider the statement : q : For any real numbers a and b, a2 = b2⇒ a = b By giving a counter-example, prove that q is false.
Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.
write each of the following using ‘if and only if’ : (i) In order to get A grade, it is necessary and sufficient that you do all the homework regularly. (ii) If you watch television, then your mind is free, and if your mind is free, then you watch television.