Check whether the following statement is true or not. If x, `y in Z`are such that x and y are odd, then xy is odd.

Explanation

We assume that p is true and show that q is true p is true means x and y are odd integers. Then ,

x=2m+1 for some integer m and y =(2n+1) for some integer n,

∴xy=(2m+1)(2n+1)

=(4mn+2m+2n+1)

=2(2mn+m+n)+1,

which is clearly odd.

Thus,
p⇒q.

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