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Math Help - prove without set algebra

  1. #1
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    prove without set algebra

    prove without set algebra:

    A \ (A ∩B)=(A \ B)

    this is my solution:

    consider A \ (A ∩B)

    let x ∈ A and x ∉ A
    --> x ∈ B'
    --> x
    ∈ A\B

    is this correct?
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  2. #2
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    Re: prove without set algebra

    First, you showed only one inclusion: $A\setminus (A\cap B)\subseteq(A\setminus B)$. Second, could you explain more why $x\in A$ and $x\notin A\cap B$ imply that $x\notin B$? This problem is elemenratu enough so that every step has to be spelled explicitly.
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