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Math Help - Proving identities without Venn diagrams

  1. #1
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    Proving identities without Venn diagrams

    Hi,

    We are having some problems proving identities without Venn diagrams and wonder if anyone can help.

    A\B = A\(AnB)

    We can do this using Venn diagrams but have no idea how to do it without.

    Thanks for any help.
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  2. #2
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    Quote Originally Posted by jnick View Post
    We are having some problems proving identities without Venn diagrams and wonder if anyone can help.
    A\B = A\(AnB)
    A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)
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  3. #3
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    Quote Originally Posted by Plato View Post
    A\setminus B=A\cap B^c=A\cap(A^c\cup B^c)=A\setminus(A\cap B)
    Hi,

    Thanks for the quick reply. Could you explain what B^c means as we haven't seen this symbol before and can't find it in our text book(Rosen). Thanks again.
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  4. #4
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    Quote Originally Posted by jnick View Post
    Could you explain what B^c means as we haven't seen this symbol before and can't find it in our text book(Rosen).
    It means complement. Rosen uses \overline{B} for the same notation.
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  5. #5
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    Quote Originally Posted by Plato View Post
    It means complement. Rosen uses \overline{B} for the same notation.

    Perfect. Thanks for the help!
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