Question

Proof of sum of even and odd number is always odd using contradiction

Answer 1

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Here's the answer:

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STATEMENT : Sum of an odd No. an Even No. is Always Odd

PROOF BY CONTRADICTION:

Assume that sum of odd number and even number is even.

Assume an Odd No. of form 2m+1 ;
where m>0

Also Assume an Even No. 2n ; n>0

We aren't assuming any statement that whichever is greater or smaller.

As it doesn't affect the result I.e., Sum

So,
2m+1 + 2n = 2k (say)

Solving the Equation on LHS gives:
2(m+n) + 1

Clearly Value on the LHS is of the form 2a + 1 ; where a = m + n.

So LHS is an Odd No. where RHS is an Even No.

So The Hypothesis we made is wrong.

Thus it is loved that sum of an odd number and even number is always ODD.

------ HENCE PROVED --------

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