First proof. If m is an even integer, and n is an odd integer, then m+n is odd.
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Does it help if I tell you that every even integer can be written as \(m=2k\) (since it's divisible by 2) and every odd integer can be written as \(n=2l+1\)?
So to prove that \(m+n\) is odd you somehow want to show from what I told you about \(m\) and \(n\) that it can be written as \(2c+1\) for some integer \(c\).
ok im still lost if you could do this one, i have a couple more to do and i just need an example to go off of.
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Okay, so if we use what I said, we can write \(m=2a\) and \(n=2b+1\). Then we also have
But if we put \(c=a+b\) we see that \(m+n=2c+1\), this is the form of a odd number, so \(m+n\) must be odd. QED.
wow i just didnt know what i was doing, after i finished your example they were so easy. thank you.