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Math Help - Show that if A and B are sets then...

  1. #1
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    Show that if A and B are sets then...

    if A and B are sets, then (A n B ) U ( A n B ) = A

    the 2nd B has a _ on the top. the n is supposed to be an upside down U

    How would i go about showing this.
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  2. #2
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    Quote Originally Posted by tyrone92 View Post
    if A and B are sets, then (A n B ) U ( A n B ) = A

    the 2nd B has a _ on the top. the n is supposed to be an upside down U

    How would i go about showing this.

    (A\cap B) \cup (A\cap \overline{B})=A

    The general strategy for proving 2 sets are equal is to prove that all of the elements in the one on the left are also in the one of the right and viceversa


    So, let x\in (A\cap B) \cup (A\cap \overline{B})

    Then by definition of union, x\in (A\cap B) or x\in (A\cap\overline{B})

    If x\in (A\cap B) then x\in A and x\in B by definition of intersection. Therefore x\in A

    If x\in (A\cap\overline{B}) then x\in A and x\in\overline{B} by definition of intersection. Therefore x\in A

    Now you should try going the other way. Does the question state B is subset of A? or a subset of X, to give the complement meaning?
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  3. #3
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    Quote Originally Posted by tyrone92 View Post
    if A and B are sets, then (A n B ) U ( A n B ) = A
    the 2nd B has a _ on the top. the n is supposed to be an upside down U
    How would i go about showing this.
    (A\cap B)\cup(A\cap\overline{B})=A simply says the any element in A is either in B or not in B.
    Can you write that up?
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