The domain of this relation is the intergers Determine the t

The domain of this relation is the intergers. Determine the truth value of each of the following. Give a reason for the answer.

Solution

Answer:

Let m and n be integers (universal instantiation). Assume m and n are even (hypothesis of the argument). Since even integers are multiples of two we may write m = 2k and n = 2` where k, ` 2 Z. Using algebraic properties of integers we have m + n = 2k + 2` = 2(k + `). This shows m + n is a multiple of two and so it is an even integer.