Question

Use a direct proof to show that the sum of two odd integers is even

Answer 1

Below is the proof that the sum of two odd numbers is always even.

How to prove that the sum of two odd numbers is even?

First, remember that an even number is written as:

x = 2*n

Where n is an integer number.

While an odd number will be written as:

y = 2*n + 1

Now, let's say that we have two odd numbers:

A = 2k + 1

B = 2n + 1

If we add these we get:

A + B = (2k + 1) + (2n + 1) = 2k + 2n + 2 = 2*(k + n + 1)

And k + n + 1 is an integer number, then we can write:

k + n + 1 = N

So we get:

A + B = 2N

Then the sum of A and B is an even number.

Thus, we proved that for the sum of any two odd numbers, the outcome will always be even.

If you want to learn more about odd numbers, you can read:

brainly.com/question/543861