Question

If both x and y are both odd numbers, prove that their sum is always an even number.

Answer 1

Answer: The sum of two odd numbers is an even number.

Explanation:

Some examples:

3(odd)+3(odd)=6(even)

29(odd)+9(odd)=38(even)

Answer 2

x + y is an even number. /proved

Explanation:

If x and y both are odd numbers, then they can be written as,

x = 2a + 1

y = 2b + 1 (where a and b are integers)

The sum of x and y is,

x + y = (2a + 1) + (2b + 1)

= 2a + 2b + 2

= 2(a + b + 1)

Since a and b are both integers, the expression (a + b + 1) is also an integer.

Therefore, x + y is an even number.