First proof. If m is an even integer, and n is an odd integer, then m+n is odd.

Question

dape · Answer

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 $n=2l+1$?

dape · Answer

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 $c$.

anonymous · Answer

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.

dape · Answer

Okay, so if we use what I said, we can write $m=2a$ and $n=2b+1$. Then we also have
$$m+n=(2a)+(2b+1)=(2a+2b)+1=2(a+b)+1$$
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.

anonymous · Answer

wow i just didnt know what i was doing, after i finished your example they were so easy. thank you.

dape · Answer

Awesome, glad I could help :)