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Homework Help: Discrete math proof

  1. Feb 16, 2015 #1
    1. The problem statement, all variables and given/known data
    Prove that the following four statements are equivalent:
    (a) n2 is odd.
    (b) 1 − n is even.
    (c) n2 is odd.
    (d) n2 + 1 is even.

    2. Relevant equations

    None really, just the use of different proofs ( indirect, etc...)
    3. The attempt at a solution

    I'm having trouble with this one because of (2) things. First, the question makes no sense ( unless I'm reading it wrong) because, as I understand it now, it is asking to prove all statements are equivalent BUT 2 of them are eve and the rest is odd. Secondly, I'm having trouble with it because of the definition that n=2k is EVEN and n=2k+1 is odd because I tried this:

    Supposle n is odd.
    n=2k therefore n=(2k)2= 22k2 = 2(2k2) which goes against the definition.

    Can anyone point me in the right direction?
  2. jcsd
  3. Feb 16, 2015 #2


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    Uh ... are you sure you copied (a) and (c) correctly?
  4. Feb 16, 2015 #3
  5. Feb 16, 2015 #4


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  6. Feb 16, 2015 #5
    not at all, my assumption of n being even was just wrong, but that's all I've been taught before so I thought it was a set definition. anyway case closed.
  7. Feb 16, 2015 #6


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    You misunderstand. You copied the problem incorrectly. Do you not see the obvious mistake?
  8. Feb 16, 2015 #7
    I somehow read d... definitely sorry about that. I'll go crawl in a hole now.
  9. Feb 19, 2015 #8


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    " I'll go crawl in a hole now." Can't see any reason to do that! Just change c) to n3 is odd , then carry on. No need to worry about a trivial typo.

    So, " n=2k therefore n=(2k)2 " what makes you say that?
    It's just like saying n=n2 which is not generally true.
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