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Math Help - Sets

  1. #1
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    Sets

    Can anyone give me an example of two sets A and B such that A intersection B is empty but A complement intersection B complement is not?
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  2. #2
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    Re: Sets

    Hey jcir2826.

    Let A and B = 0, A' and B = v. This means that (A and B) and (A' and B) = B = 0. So B is the empty set.

    This means that for any A', A' and B = 0 since B is the empty set.

    So its not possible to satisfy your condition.
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  3. #3
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    Re: Sets

    I will also denote the complement of X by X'.

    Quote Originally Posted by chiro View Post
    Let A and B = 0, A' and B = v. This means that (A and B) and (A' and B) = B = 0. So B is the empty set.
    The OP needs A' ∩ B' ≠ ∅, not A' ∩ B ≠ ∅. Also, what is v and why is (A and B) and (A' and B) = B?

    A' ∩ B' ≠ ∅ holds for most A and B, more precisely, unless A ∪ B is the whole universal set. So, you just need to find two small disjoint sets.
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  4. #4
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    Re: Sets

    Quote Originally Posted by jcir2826 View Post
    Can anyone give me an example of two sets A and B such that
    A intersection B is empty but A complement intersection B complement is not?
    .

    Surely that says A\cap B=\emptyset\text{ but }A'\cap B'\ne\emptyset.
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  5. #5
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    Re: Sets

    Let U= {a, b, c, d}, A= {a}, B= {b}. then A complement is {b, c, d} and B complement is {a, c, d}. There intersection is {c, d}.


    In fact, any example where A\cup B is not the universal set will do.
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