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Given two propositions, p and q, start out with p implies q. For example if a number is even it is a multiple of 2. So we are saying even implies multiple of 2.

Now the contrapositive is not p implies not q so if a number is not even it is not a multiple of 2. Or if not p then not q.

The contrapositive of the contrapositive would negate a negation so that would make it positive.

If not (not p) then not(not q) or in other words, you are back where you started, p implies q.

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