Question

For all integers m and n, if m + n is even, then either m and n

are both even, or m and n are both odd.

Answer 1

If the sum of two integers is even, then either both integers are even or both integers are odd.

Step-by-step explanation:

In mathematics, if the sum of two integers, m + n, is even, then either both m and n are even or both m and n are odd. This can be proven by considering the two possible cases. If m and n are both even, then they can be written as m = 2a and n = 2b, where a and b are integers. The sum of m and n is then 2a + 2b = 2(a + b), which is an even number. Similarly, if m and n are both odd, they can be written as m = 2a + 1 and n = 2b + 1, where a and b are integers. The sum of m and n is then 2a + 1 + 2b + 1 = 2(a + b + 1), which is also an even number.