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Math Help - A Proof for a Conditional Statement

  1. #1
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    A Proof for a Conditional Statement

    Use the element method for proving a set equals the empty set. Assume that all sets are subsets of a universal set U.

    1.) For all sets A and B, if B subset of A compliment then A intersection B = the empty set.

    2.) For all sets A, B, and C, if B subset C and A intersection C = the empty set then A intersection B = the empty set.
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  2. #2
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    Quote Originally Posted by loutja35 View Post
    Use the element method for proving a set equals the empty set. Assume that all sets are subsets of a universal set U.

    1.) For all sets A and B, if B subset of A compliment then A intersection B = the empty set.

    2.) For all sets A, B, and C, if B subset C and A intersection C = the empty set then A intersection B = the empty set.
    Here is what is expected using the element method.
    If x\in B then because B\subseteq A^c then x \notin A.
    Hence x\notin A\cap B or A\cap B=\emptyset.

    You try the next one.
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    I'm sorry, I still don't understand the proof behind this. Could you further explain?
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  4. #4
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    Quote Originally Posted by loutja35 View Post
    I'm sorry, I still don't understand the proof behind this. Could you further explain?
    First what exactly is meant by the element method?
    I assumed it was the same an pick-a-point?

    I personally think that this is best done by contradiction.
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