Question

prove that the sum of two odd numbers is always even by two different methods​

Answer 1

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• Let the two odd numbers be, 2a+1 and 2b+1. So, 2a+1 + 2b+1 = 2(a+b)+2 = 2(a+b+1), which is even.

Hence, proven.

Answer 2

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Let x and y be two odd numbers. 

Then x=2m+1 for some natural number m and y=2n+1 for some natural number n.

 Lets take out their sum.

Thus x+y=2m+1+2n+1=2(m+n+1)Here with the addition 2 in there.

Therefore, x+y is divisible by 2 and is even.

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