Question

What is the sum of any two even numbers?

Answer 1

Hint: Assume the numbers taken for evaluation to be even. Though the contradiction method can also be used. But this is simpler comparatively.

Let us assume any two integers. We can write them as $2x$and $2y$.
 The sum of these two even numbers is$2x + 2y$ .
Now, Take 2 common . That means $2x + 2y = 2(x + y)$.
Inside the parenthesis, we have a sum of two integers. Since the sum of two integers is just another integer then we can let an integer $n$ be equal to $(x + y)$ .
Substituting $(x + y)$ by $n$ in $2(x + y)$, we obtain $2n$ which is clearly an even number. Thus, the sum of two even numbers is even.
For example, 2+2=4, 2(3)+2(5)=16, etc.

Note: In these types of questions, we need to make an assumption and then evaluate the corresponding steps to reach the final proof.