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Math Help - Help with Sets

  1. #1
    Newbie
    Joined
    Jan 2009
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    3

    Help with Sets

    Please tell me that the following statement is true or false :

    (AB) (AB) = A

    I think it should be
    (AB) (AB) = A - B

    Please help.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, goodone!

    Is the following statement is true or false?

    (A \cup B) \cap (A \cap B')

    I think it should be: . A - B . . . . Right!
    I'll let you supply the reasons . . .


    . . \begin{array}{cccc}<br />
(A \cup B) \cap A \cap B' \\ \\<br />
(A\cup B) \cap B' \cap A \\ \\<br />
\bigg[(A \cap B') \cup (B \cap B')\bigg] \cap A \\ \\<br />
\bigg[(A \cap B') \cup \emptyset\bigg] \cap A \\ \\<br />
(A \cap B') \cap A \end{array}

    . . . . . \begin{array}{cc}A \cap (B' \cap A) \\ \\<br />
A \cap (A \cap B') \\ \\<br />
(A \cap A) \cap B' \\ \\<br />
A \cap B' \\ \\<br />
A - B<br />
\end{array}


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