2 DISCRETE MATH please help me answer this next question and

(2) DISCRETE MATH: please help me answer this next question and be as specific as possible (show all of your work) because I will be putting it in my study guide for the class. thank you very much!

Exercise #4. (10 pts) Let m be an even integer and n be an even integer. Prove that their sum is even.

Solution

Let m and n be even integers.

By definition of even we have that m = 2b and n = 2a.

Consider the sum m + n = 2b + 2a = 2(b + a) = 2k where k = a + b is an integer.

Therefore by definition of even we have shown that my hypothesis is true.