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Math Help - Question about a few explanations i do not understand.

  1. #1
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    Question about a few explanations i do not understand.

    since 3n+2 is even so is 3n
    how is 3n even?? and how is 3n+2 even?

    if we add subtract an odd number from an even number ,we get an odd number so 3n - 2 = 2n is odd??? i don't get this at all

    then it follows that but this is obviously not true, there fore our supposition was wrong, and the proof by contradiction is complete.

    i'm so lost i don;t understand what is being said and it is getting really frustrating please help me understand this in English.
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  2. #2
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    Quote Originally Posted by camboguy View Post
    since 3n+2 is even so is 3n
    how is 3n even?? and how is 3n+2 even?
    Well for all n \in \mathbb{Z} this is not true. Consider n = 1 \implies 3\times 1+2 = 5

    But if n itself is even then this could be true, do you have any other information?
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    the question is asking me to prove that if n is an integer and 3n+2 is even, then n is even using contradiction.

    i just posted another thread about how i don't understand what contradiction is and iv been trying a few days now to understand what it is and wanted to do it on my own but its just breaking me down and i just don't understand what contradiction is.
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  4. #4
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    In a proof by contridiction you take the orignal claim 3n+2 is even and negate it. Then show that leads to a contridiction. You can then imply the opposite is true.

    Here's some examples Proof by contradiction - Wikipedia, the free encyclopedia

    In this particular proof for \forall n \in \mathbb{Z}, 3n+2 is even given n is even you just need to use some simple logic.

    You are told n is even so start with n=2k, k \in \mathbb{Z} , now 3n+2 = 3(2k)+2 = 6k+2 = 2(3k+1) and you are finished.
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    if i am eating then i am watching tv.

    if i am not eating then (i would have to find something that states that i am watching tv and now watching tv at the same time?) << would this be the contradiction i am trying to find?
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