Question

Please answer this as a proof and show work! thanks

2. Prove that an odd number times an even number is even.

Answer 1

Answer with Step-by-step explanation:

Let m be the odd number.

So, for any x ∈ Z , we get that

m = 2x+1

Let n be the even number.

So, for any y ∈  Z, we get that

n = 2y

So, According to question, the odd number times an even number is given by

$nm=(2x+1)(2y)\\\\nm=2(2xy+y)$

So, by the definition of even numbers, we get that nm is even.

Hence,  an odd number times an even number is even.