How to determine which methods to use when proving a stateme

How to determine which methods to use when proving a statement?

I have learned direct, contrapositive, and contradiction methods of proving a statement but how do I determine which

method to use just by looking at the proposition?

Solution

First of all you should try to prove a statement by direct proof. Which means that for given hypotheses try to argue directly that the conclusion follows. This turns out to be the best method when the hypotheses can be translated into equations which further can be used to give other sufficient algebraic expressions to prove that the conclusion follows. Generally when we are given positive premises and we have to follow positive conclusion then we can use this method very easily.

If a direct proof seems tuff or if premises and conclusion all are negative, then we should try to use the contrapositive method.

If the above two methods are tuff to prove that conclusion follows, then you should try to use proof by contradiction. If we are given premises positive and conclusion negative or the other way around, then this method works very well. In this method of proof we assume the hypotheses are true and the conclusion is false and try to arrive at a contradiction.