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Math Help - open and closed sets proof

  1. #1
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    open and closed sets proof

    Suppose that A and B are subsets of ℝ such that A is open and B is closed. Prove that A-B is open and B-A is closed. hint: use the fact that if X and Y are subsets of ℝthen X-Y=X∩(ℝ-Y). PLEASE SHOW ME THE LIGHT!!
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  2. #2
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    For set difference A\backslash B = A \cap B^c \,\& \,B\backslash A = B \cap A^c.

    Recall that the complement of a closed set is an open set and the intersection of two open sets is an open set.

    Recall that the complement of an open set is a closed set and the intersection of two closed sets is a closed set.
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  3. #3
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    Quote Originally Posted by Plato View Post
    For set difference A\backslash B = A \cap B^c \,\& \,B\backslash A = B \cap A^c.

    Recall that the complement of a closed set is an open set and the intersection of two open sets is an open set.

    Recall that the complement of an open set is a closed set and the intersection of two closed sets is a closed set.
    haha I don't know what this means. My discrete professor gave it to us an extra credit assignment. I can't figure out this neighborhood, boundary, etc etc stuff. Can anyone offer a completed proof?
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    Quote Originally Posted by gatesamatic View Post
    My discrete professor gave it to us an extra credit assignment. I can't figure out this neighborhood, boundary, etc etc stu
    This is my own take on this.
    These are questions about basic topology.
    I do not think that topics in topology have any place in a course on discrete mathematics.
    Your instructor gave you something beyond your grasp.
    The sad truth is: it may enhance her/his on importance without doing anything for you.
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