Odd Number multiplied by Even Number is Even

Theorem

 * If an odd number by multiplying an even number make some number, the product will be even.

Proof
Let $a$ be odd and $b$ be even.

Then by definition of odd number:
 * $\exists c \in \Z: a = 2 c + 1$

and by definition of even number:
 * $\exists d \in \Z: b = 2 d$

So:

Hence the result by definition of even number.