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Math Help - Question about sets

  1. #1
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    Question about sets

    If I have ((A ∩ B) ∪ Ω), is that equivalent to Ω ?
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    Re: Question about sets

    Quote Originally Posted by Nombredor View Post
    If I have ((A ∩ B) ∪ Ω), is that equivalent to Ω ?
    Well of course, if X\subset Y then X\cup Y=Y~.
    All set are subsets of \Omega.
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    Re: Question about sets

    And I am right in saying that (A -B) ∪ (B - A) is equivalent to (A ∪ B) - (A ∩ B) ?

    And is it accurate to say that (A ∩ Ω) ∪ ~B is the same as Ω - B ?
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    Re: Question about sets

    Quote Originally Posted by Nombredor View Post
    And I am right in saying that (A -B) ∪ (B - A) is equivalent to (A ∪ B) - (A ∩ B) ?
    That is correct.

    Quote Originally Posted by Nombredor View Post
    And And is it accurate to say that (A ∩ Ω) ∪ ~B is the same as Ω - B ?
    If ~B means B^c, the complement of B then no.
    (A\cap\Omega )\cup B^c=A\cup B^c which is not necessarily B^c~.
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    Re: Question about sets

    ~B means ''non B'' in this case.
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    Re: Question about sets

    Quote Originally Posted by Nombredor View Post
    ~B means ''non B'' in this case.
    "non B" is not a set theory term.
    B complement is the set of all elements not in B.
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    Re: Question about sets

    Quote Originally Posted by Plato View Post
    (A\cap\Omega )\cup B^c=A\cup B^c which is not necessarily B^c~.
    How do they look different on a Venn diagram ?
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    Re: Question about sets

    Also, I was wondering whether I was right in saying that (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
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    Re: Question about sets

    The only thing I've ever seen big-omega used for in set theory is as another name for omega-1 (first uncountable ordinal). Does it also mean "universal set" in the context of intro set theory, then?
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    Re: Question about sets

    Quote Originally Posted by Annatala View Post
    Does it also mean "universal set" in the context of intro set theory, then?
    Yes, that's what I meant it as. I've also seen people use just ''u'', but I prefer omega because ''u'' also looks a lot like the reunion symbol.
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    Re: Question about sets

    double post
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  12. #12
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    Re: Question about sets

    Quote Originally Posted by Nombredor View Post
    Also, I was wondering whether I was right in saying that (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
    it is correct
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    Re: Question about sets

    Quote Originally Posted by Nombredor View Post
    Also, I was wondering whether I was right in saying that (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
    No that is not correct.
    Let \Omega =\{1,2,3,4,5,6,7,8,9\},~A=\{1,2,3,4\}~\&~B=\{2,4,6  ,8\}.

    Find (A\cup B)~\&~(A\cup B^c).

    What is their intersection? What is A-B~?
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    Re: Question about sets

    it is equal to A
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    Re: Question about sets

    Quote Originally Posted by Amer View Post
    it is equal to A
    Correct. So the OP
    Quote Originally Posted by Nombredor View Post
    I was right in saying that
    (A ∪ B) ∩ (A ∪ ~B) is equivalent to (A - B) ?
    Is incorrect.
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