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Short hand interval notation

  1. Feb 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the following intervals:

    A = [-3,5), B = (3,8), C = (0,4]

    Find: A[itex]\cap[/itex]B and A[itex]\cap[/itex]C

    3. The attempt at a solution

    I thought that: A[itex]\cap[/itex]B=(3,5) and that A[itex]\cap[/itex]C=[0,4] as that is the intersection point, but this book (Schaum's Probability Outlines) says that A[itex]\cap[/itex]B=[-3,8) and A[itex]\cap[/itex]C=[-3,5)

    I'm looking to confirm that the book might be wrong (Amazon reviews indicate alot of typographical errors) and instead maybe their answer refers to [itex]A\cup B[/itex] and [itex]A\cup C[/itex] perhaps? Or am I getting confused?

    Thanks!!
     
  2. jcsd
  3. Feb 18, 2012 #2
    The book answers are for union [itex]\cup[/itex], and you are really close to correct with your answers for intersection [itex]\cap[/itex]. It could be a typo in either question or answer.
     
  4. Feb 18, 2012 #3

    HallsofIvy

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    Yes, [itex]A\cap B= (3, 5)[/itex] while [itex]A\cup B= [-3, 8)[/itex] as Joffan says. [itex]A\cup C= [-3, 5)[/itex]. But [itex]A\cap C[/itex] is NOT [0, 4] because 0 is not in C.
    In fact, C is a subset of A so [itex]A\cap C= C[/itex] and [itex]A\cup C= A[/itex].
     
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