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.

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.

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.

By giving a counter-example, show that the statement is false :

p : If n is an odd positive integer, then n is prime.

Use contradiction method to prove that :

is irrational

is a true statement.