Question

prove that the product of 2 odd natural numbers is odd

Answer 1

Answer:

Step-by-step explanation:

Let a and b be two odd numbers....

If a and b are odd, then a and b can be written as:

a=2m+1 ,

b=2n+1

Where m and n are whole numbers.

So....

ab=(2m+1)(2n+1)

=4mn+2m+2n+1

=2(2mn+m+n)+1

Which is odd.

Bcz it leaves the remainder 1 after being divided by 2....

Hope it helps....:-)

Answer 2

Answer:

Step-by-step explanation:

Consider the sum a + b = (2n + 1) + (2m +1) = 2n + 2m +2 = 2k, where k = n + m + 1 is an integer. Therefore by definition of even we have shown that a + b is even and my hypothesis is true. 5) The product of two odd integers is odd. Proof: Let n and m be two odd integers.