Question

show that these statements about the integer x are equivalent: (i) 3x 2 is even, (ii) x 5 is odd, (iii) x2 is even.

Answer 1

All the above statements are proved using proof by contraposition.

What is proof by contraposition?

Proof by contrapositive, also known as proof by contraposition, is an inference technique used in mathematics where a conditional statement's contrapositive is used to infer the conditional statement's conclusion. To put it another way, the conclusion "if A, then B" is inferred by building a proof of the claim "if not B, then not A" instead. This method is frequently chosen if the contrapositive is more straightforward to establish than the first conditional statement.

The term "contraposition" describes a proving strategy known as "proof by contraposition," which involves drawing an inference from a conditional statement to its logically equivalent contrapositive. The antecedent and consequent of a sentence are inverted and flipped in the contrapositive.

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