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Homework Help: Set Notation/Theory help

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data

    Three tests are available to identify six different substances.

    Test 1 is true in the presence of substance 1,2,3, and 4
    Test 2 is true in the presence of substance 3,4, and 5
    Test 3 is true in the presence of substance 2,5, and 6

    Using set notation to denote the events that a substance under test is

    a) substance 1
    b) substance 2
    c) substance 6

    2. Relevant equations

    Let [itex]E_{i}[/itex] denote the event that the i'th test is positive, [itex]i= 1, 2, 3[/itex]

    3. The attempt at a solution

    How do I properly represent the answers in set notation?

    Currently here are my attempts at a,b, and c.

    a) [itex] S_{1} = E_{1}[/itex] [itex]\cap[/itex] [itex]E_{2}^{'}[/itex] [itex]\cap[/itex][itex]E_{3}^{'}[/itex]

    b) [itex] S_{2}[/itex] cannot be identified

    c) [itex] S_{6} = E_{3}[/itex] [itex]\cap[/itex] [itex]E_{2}^{'}[/itex] [itex]\cap[/itex][itex]E_{1}^{'}[/itex]

    Is this how you correctly write the answer in set notation?

    Also with b) I am also unsure of my answer. Would it be correct to say that E1 is true AND not S6?
  2. jcsd
  3. Feb 28, 2014 #2


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    You haven't said what ##S_i## means, but if ##S_i=\{i\}## then a) and c) look ok. For b) substance two is the only one that is true for tests 1 and 3, isn't it?
    Last edited: Feb 28, 2014
  4. Mar 1, 2014 #3
    doh! I see. Thank you :)

    How about the notation? Is the way that I represented the answers correct?
  5. Mar 1, 2014 #4


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    I don't know what your class expects, but if you define the sets as you have then the relations you have written are correct.
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