Valid Reasoning

Question

How do you use a direct proof to show that the sum of two even integers is even?

Answer 1

1. Let m and n be even integers                                        1. Given

2. ∃ integers k and j such that m=2k and n=2j                    2, definition of even numbers

3. m+n=2k+2j                                                                 3. "algebra"

4. m+n = 2(k+J)                                                              4. factor 2

5. k+j is an integer                                                           5. integers are closed under addition

6. m+n is even                                                                6. definition of even number                    

 

Any questions feel free to add a comment.

 

Answer 2

Even integers are 2, 4, 6, 8, 10, 12 and so on. 

 

2 + 4 = 6

 

6 is even.

 

 

2 + 1 = 3

 

1 is odd.  The sum is NOT even.