1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook