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Simple Set Operation

  1. Oct 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Let U= all real numbers, A=[2,9), B=(0,1], C=[-1,4]. Express in interval notation: (A union B) - C


    2. Relevant equations
    A union B includes all elements that are in either A or B, including any objects that happen to lie in both A and B.

    The difference A - B consists of all objects that are elements of A and are not elemnts of B

    3. The attempt at a solution

    I think the interval is from (4,9). A union B would be (0,1]union[2,9], then you remove from [-1, 4]. The only reason why I don't know if I'm right is because of the gap in the union of A and B. I don't know if that has any effect on the answer.

    If (4,9) is correct then would it be safe to assume that (A union B) - C = A-C ?
     
  2. jcsd
  3. Oct 1, 2007 #2

    CompuChip

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    Your reasoning is correct.
    Indeed in this case, [tex](A \cup B) - C = A - C[/tex], because B is completely contained within C. So whatever elements from B you add to A when taking the union, you take them out again when removing C.
    Of course, this is in general not true (e.g. A = [0, 1], B = [1, 2], C = [0, 1/2) is a counter example).

    The gap in the union doesn't matter: X - Y is defined as the set of all elements which are in X but not in Y.
     
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