anonymous
  • anonymous
First proof. If m is an even integer, and n is an odd integer, then m+n is odd.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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dape
  • dape
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
  • dape
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
  • anonymous
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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dape
  • dape
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
  • anonymous
wow i just didnt know what i was doing, after i finished your example they were so easy. thank you.
dape
  • dape
Awesome, glad I could help :)

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