Question

Find the smallest distinct positive numbers that provide a counterexample to show the statement is false.The sum of any two different odd numbers plus any even number is odd.

Answer 1

The sum of two even or odd numbers ALWAYS gives an even number.

We'll run a test with 1,2 and 3.

Odd numbers: 1, 3

Even number: 2

Adding the odd numbers, we get 1 +3 = 4.

Adding it to the even number, we get 4 +2 = 1 + 3 + 2 =6

The general form of an odd number = 2n + 1

The general form of an even number = 2n

Adding 2 odd numbers give 2(2n + 1) = 4n + 2

Adding to an even number; 4n + 2 + 2n

Giving 6n + 2

Any number of the form above is an even number

The statement is thus false.