Question

What is the converse, inverse, and contrapositive statement: If two numbers are odd,their product is odd

Answer 1

Answer:

The converse of the conditional statement is “If Q then P.” ... The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not .

Is this valid proof? Proof by contrapositive. The contrapositive of the implication is: ∀x,y∈Zif x and y are not both odd then x×y is even.

To prove the contrapositive of the implication, let x=2k for some arbitrary k∈Z. We cannot assume anything about y to keep generality. Then x×y=2k×y=2ky=2(ky). Because x×y is a multiple of 2 the implication holds.