Question

check whether the following statement is true or false by contrapositive method
"if x and y are odd integers,then xu is odd "

Answer 1

I think yes when multiple odd numbers as a product we get odd

Answer 2

Let x and y be integers. Prove that if x*y is odd, then x and y are odd.

I assume that x and y are odd, i.e. x=2a+1 and y=2b+1.

Then, xy=(2a+1)(2b+1)

= 4ab+2a+2b+1

= 2(2ab+a+b)+1

= 2c+1, for some integer c