Question

The sum of two odd numbers is always an even number. True or False?

Answer 1

The statement "The sum of two odd numbers is always an even number" is True.

To understand why, let's break down the properties of odd and even numbers:

1. Odd Numbers: An odd number is an integer that is not divisible by 2. Mathematically, any odd number can be expressed as
`2n+1`, where
`n` is an integer. For example, if
`n=1`, the odd number is
`2`×
`1+1=3`.

2. Even Numbers: An even number is an integer that is divisible by 2. It can be expressed as
`2m`, where
`m` is also an integer.

Now, consider two odd numbers. Let's represent them as
`2n+1` and
`2m+1`, where
`n` and
`m` are integers. The sum of these two odd numbers would be:

`(2n+1)+(2m+1)`

Let's simplify this expression:

`=2n+2m+2`

`=2(n+m+1)`

Notice that the sum,
`2(n+m+1)`, is a multiple of 2. This means the sum of any two odd numbers is always an even number, because it can be expressed as 2 times another integer. Hence, the statement is true.

Answer 2

Answer: True

Examples:

• 5+3 = 8
• 17+5 = 22
• 9+29 = 38
• 1+5 = 6

---------------

Here's a proof:

Let k and m be two integers

2k+1 and 2m+1 are odd integers

Add them up.

(2k+1)+(2m+1)

= 2k+2m+2

= 2*(k+m+1)

= 2*(some integer)

= some even integer

This proves that adding any two odd numbers gets an even number.