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Math Help - proves -discrete math !!! please help!!!

  1. #1
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    Question proves -discrete math !!! please help!!!

    1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then aČ│bČ

    2. Prove: for all n ϵ Z, n is add if and only if nČ is odd.

    3. using the definition of equal sets and the definition of subset, prove this

    form of DeMorgan's Law:____ _ _
    If A and B are sets then AUB=A∩B


    Please help!!!!
    Last edited by olenka; October 14th 2008 at 02:54 PM.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by olenka View Post
    1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then aČ│bČ
    If a|b, then b=ka
    square both sides =)

    2. Prove: for all n ϵ Z, n is odd if and only if nČ is odd.
    If n is even, then n=2n' ---> nČ=...
    If n is odd, then n=2n'+1 ---> nČ=...

    3. using the definition of equal sets and the definition of subset, prove this

    form of DeMorgan's Law:____ _ _
    If A and B are sets then AUB=A∩B
    A \cap B \subseteq A \cup B

    This may be all you need eh ?
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  3. #3
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    Question ehhhh ....help

    Quote Originally Posted by Moo View Post
    Hello,

    If a|b, then b=ka
    square both sides =)


    If n is even, then n=2n' ---> nČ=...
    If n is odd, then n=2n'+1 ---> nČ=...


    A \cap B \subseteq A \cup B

    This may be all you need eh ?
    Hi, thanks for that , but could U be more specific...and show me exactly step by step process of solving that problems??? Thanks!!
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  4. #4
    Moo
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    Quote Originally Posted by olenka View Post
    Hi, thanks for that , but could U be more specific...and show me exactly step by step process of solving that problems??? Thanks!!
    Yo,

    What don't you understand exactly ? Have you at least tried to do them ?
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  5. #5
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    Question discrete math already done! please check if it's right!

    1. Prove: for all a ϵ Z, for all b ϵ Z if a│b then aČ│bČ

    We say a divides b denoted by ab if there exist a k such that b=ak kεZ by definition of divides. then , so , therefore,
    by closure property of multiplication. Since m is an integer, then mb^2 is an integer. Thus,aČ is expressed as m times b square, so by def of divides aČ│bČ . So by real number properties for all integers a and b ϵ Z if a│b then aČ│bČ.

    if there is an mistake anywhere...please correct me. Thank you so much!!!
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