Answer this as a proof and show work!
2. prove that an odd number times an even number is even.

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

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

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