If m is an even # and n is an odd #, then m+n=odd#. Prove this is wrong.

Question

I need to prove that this statement is correct. I've plugged in integers into the formula but I just see that the formula seems correct (Ex 10+3=13). My teacher wants me to prove it is incorrect so I am really confused about it.

Answer 1

Every even number can be represented as 2j, where j is any integer

Every odd number can be represented as 2k+1, where k is any integer.

so, according to question:

2k + 2j+1 = 4k +1 = 2(k+j) +1 = 2m +1, where m =k+j

So, whenever we add one even number with an odd number we will always get an odd number, no matter what. The teacher has given you a trick question, and probably wanted to test your knowledge at that time.

Though this answer may be of no use to you at this time, but it may help others, so I am leaving this answer.

Comments

Using k in the representation of the numbers implies a relationship between the numbers. So, for example, the numbers could be represented by 2j and 2k+1, where j and k are integers, then their sum would be 2(j+k)+1 which is an odd number (2m+1) by definition. Yes, the teacher was probably trying a trick question.

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Oops you got me, you are right, I forgot. I should have taken two different variables. I have corrected it.