Use a direct proof to show that the product of two odd numbers is odd.

yegumbi4q0

yegumbi4q0

Answered question

2022-12-29

Use a direct proof to show that the product of two odd numbers is odd.

Answer & Explanation

Alana Walsh

Alana Walsh

Beginner2022-12-30Added 7 answers

Let xandy be the two odd numbers:
And, x=2m+1andy=2n+1, where mandn are natural numbers.
On solving, we get:
x.y=(2m+1).(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1
The expression 2mn+n+m is a natural number that is multiplied by 2 that results in an even number. After adding 1it becomes an odd number.
Hence, the product of xandy is an odd number.

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