What is indirect method of proof? Example with example.
indirect method of proof – In this sub-section we shall consider two roundabout methods for proving p ⇒ q.
Proof by contrapositive: In the first method, we use the fact that the proposition p ⇒
q is logically equivalent to its contrapositive (~ q ⇒ ~ p), i.e.,
(p ⇒ q) ≡ ( ~ q ⇒ ~ p).
For instance, ‘If Ammu does not agree with communalists, then she is not orthodox.’ is the same as ‘If Ammu is orthodox, then she agrees with communalists.’.
Because of this equivalence, to prove p ⇒ q, we can, instead, prove ~ q ⇒ ~ p. This means that we can assume that ~ q is true, and then try to prove that ~ p is true. In other words, what we do to prove p ⇒ q in this method is to assume that q is false and then show that p is false. Let us consider an example.