Question

Consider the following conjecture: the sum of two even numbers will be even.
A.) give three examples supporting the conjecture. (I gave 2+2=4 4+4=8 10+10=20)
B.) Prove the conjecture( this is the part I need help with)

Answer 1

proof.
a+b = sum of even numbers
2(a/2)+2(b/2)= where a/2 and b/2 can be even or odd, or both.
2 ((a/2+b/2) ) has to be an even number, because it is evenly divislble by 2 (note the leading 2).
Therefore, the sum of two even numbers is even.