Question

b) Prove that the sum of two odd numbers is always even by two different methods.​

Answer 1

Answer: Let the two odd numbers be, 2a+1 and 2b+1. So, 2a+1 + 2b+1 = 2(a+b)+2 = 2(a+b+1), which is even. Hence, proven.

Step-by-step explanation:

Answer 2

Even numbers are those numbers that are multiples of 2 and other than even numbers are odd numbers.

Let two odd numbers be $2x+1$ and $2x+3$,

Add both the odd numbers,

$2x+1+2x+3=4x+4\\=4(x+1)$

$4(x+1)$ is the factor of even number 4.

If we, substitute any number in the value of $x$, the end result will be an even number.