Use the method of direct proof to prove the following statem

Use the method of direct proof to prove the following statement.

If two integers have the same parity, then their sum is even. (Try cases.)

Solution

Case 1: If a,b are even.

then we have a=2m and b=2n ==> a+b=2m+2n=2(m+n), which is even.

Case 2: If a,b are odd.

then we have a=2m+1 and b=2n+1 ==> a+b=(2m+1)+(2n+1)=2(m+n+1), which is also even.

hence If two integers have the same parity, then their sum is even.