Question

State true or false. The sum of three odd numbers is even.

Answer 1

Hint: Here in this question, we have to tell whether the given statement is true or false with explanation. To solve this, take any 3 odd numbers as an example when the sum of the 3 odd numbers will be even then the statement is true otherwise the given statement is false.

Complete step-by-step answer:
Even number is any number that gives a remainder of zero when divided by 2.
Examples: 0, 2, 4, 8, …

Odd number is any number that gives a remainder of 1 when divided by 2 otherwise numbers which are not divisible by two.
Examples: 1, 3, 5, 7, …

Consider the given question:
We have to check whether the statement “The sum of three odd numbers is even” is true or false.

Consider any 3 odd numbers, 1, 3 and 5

The sum of three numbers are:

\[ = \,\,1 + 3 + 5\]

\[ = \,\,9\]

Which is an odd number.

In general, by taking any 3 odd numbers their sum will be odd.

Hence, the sum of three odd numbers is odd.

Therefore, the statement is false.

Note: When we solving the problems based on even and odd numbers, we have to remember some properties they are:
The sum of two even numbers is an even number.
The sum of two odd numbers is an even number.
The sum of even and an odd number is an odd number.
The sum of three odd numbers is odd.
The sum of three even numbers is even.
Even number is divisible by 2, and leaves the remainder 0.
An odd number is not completely divisible by 2, and leaves the remainder 1.
An even number ends with 0, 2, 4, 6, and 8.
An odd number ends with 1, 3, 5, 7, and 9.