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  1. #1
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    sets

    Show that AnA'= nullset
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  2. #2
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    Quote Originally Posted by dcapdogg
    Show that AnA'= nullset
    If A=\{ \} then proof is complete.
    If A\not = \{\} then x\in A
    Then, x\not \in A' thus, A\mbox{ and }A' are disjoint thus, A\cap A'=\{\}
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  3. #3
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    Hello, dcapdogg!

    The proof depends upon what axioms and definitions are established.


    Show that A \cap A' \:=\:\emptyset

    A \cap A' is the set of elements that are in Aand in A'.

    By definition of complement: .If x \in A, then x \not\!\!{\in} A'
    . . Hence, there are no elements common to Aand A'. .They are disjoint.

    Therefore: . A \cap A' \:= \:\emptyset

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