7 Consider the statement: for all integers a and b, if a is even and b is a multiple of 3, then a b is a multiple of 6. Prove the statement. What sort of proof are you using

An integer a is even mean a = 2n for some integer n

An integer b is an multiple of 3 if b=3m for some integer m.

So for a * b is multiples of 6,

Suppose a=2n and b=3m for some integers, n, m.

Then ab=2n*3m=6 (n*m).

As n*m is an integer,

we get

ab=6 (n*m), which is a multiple of 6.

Hence Proved