SOLUTION: What is the counter example of "The sum of any 2 odd numbers is even?"

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Question 207719: What is the counter example of "The sum of any 2 odd numbers is even?"
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There's a problem with your question. There are no counter examples to prove the statement "The sum of any 2 odd numbers is even" wrong.


It turns out that any odd number can be written in the form 2x%2B1 where 'x' is a whole number. Now let's say we have two odd numbers y=2a%2B1 and z=2b%2B1 where 'a' and 'b' are whole numbers. If we add them up, we get: y%2Bz=%282a%2B1%29%2B%282b%2B1%29=%282a%2B2b%29%2B2=2%28a%2Bb%29%2B2=2%28a%2Bb%2B1%29=2k where k=a%2Bb%2B1


Now because even numbers fit the form 2x, where 'x' is a whole number, this means that 2k is an even number (since 'k' is a whole number).


So it turns out that the sum of ANY two odd numbers is ALWAYS even. This is why no counter examples are possible.