Theorem:
Prove that the product of two odd number is an odd number.
Proof:
The general form of an odd number is 2n+1, where n is an integer.
Let 2m+1 and 2n+1 are two different odd numbers, where m and n are integers.
The product = (2m+1)(2n+1)
= 2m(2n+1)+2n+1
= 4mn+2m+2n+1
= 2(2mn+m+n) + 1
(2m+1)(2n+1) = 2 (an integer) + 1 [Since, 2mn+m+n = an integer.]
= an odd number.
Directions: Solve the following problems. Also write at least ten examples of your own.
