Why is the sum of two even numbers also an even number?
Most people already know it is true, but they might not know how to prove it.
To prove this, we first need to know what an even number is. By definition, an even number is a number that is divisible by 2.
Now let’s say we have two numbers, A and B. Both are even numbers.
We can say A = 2 * x and B = 2 * y, where x and y are any two integers, we don’t really care about their value.
A + B = 2 * x + 2 * y
A + B = 2*(x+y) (by distributional property)
2*(x+y) is divisible by 2, since 2*(x+y)/2 = x+y, which x+y is integer.
Therefore, the sum of any two even numbers is also an even number.
Use this knowledge, see if you can solve Question of The Day 10/16
Now try for yourself!
Use a similar strategy to prove the sum of two odd numbers is an even number.