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Math Help - Set theory question

  1. #1
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    Set theory question

    The following question was confusing me, so if anyone could help it would be greatly appreciated!

    Suppose A, B, and C are events. Express the following events in A, B, and C.

    a) Only A occurs
    b) A and B occur, but C does not.
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  2. #2
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    Suppose A, B, and C are events. Express the following events in A, B, and C.

    a) Only A occurs A \cap B\,' \cap C\,'

    b) A and B occur, but C does not. A \cap B \cap C\,'
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    Thanks! So if I wanted to express the fact that all three events occur, I'd just do

    A intersect B intersect C?

    And if I wanted to express the fact that none of the three events occurs, I'd just do

    A' intersect B' intersect C?
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  4. #4
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    Quote Originally Posted by clockingly View Post
    Thanks! So if I wanted to express the fact that all three events occur, I'd just do
    A intersect B intersect C?
    And if I wanted to express the fact that none of the three events occurs, I'd just do
    A' intersect B' intersect C?
    Yes, with C' for the last one.
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  5. #5
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    Thanks! Sorry, one last question - how would I express the fact that exactly one of the three events occurs?

    Or the fact that at most one of the events occurs?

    I guess I'm confused about this because in each of these cases, it's not set in stone the specific events that occur (A, B, C?).
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by clockingly View Post
    Thanks! Sorry, one last question - how would I express the fact that exactly one of the three events occurs?
    use the union.

    if exactly one occurs, then that one could be A or it could be B or it could be C.

    so we have: (A \cap B' \cap C') \cup (A' \cap B \cap C') \cup (A' \cap B' \cap C)

    Or the fact that at most one of the events occurs?
    This means one or less occur. Take what i did above as an example and try to figure this one out
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  7. #7
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    Thanks!

    So if at the most one of the events occurs, you would have:

    (A intersect B' intersect C') U (A' intersect B intersect C') U (A' intersect B' intersect C') U (A' intersect B' intersect C') ?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by clockingly View Post
    Thanks!

    So if at the most one of the events occurs, you would have:

    (A intersect B' intersect C') U (A' intersect B intersect C') U (A' intersect B' intersect C') U (A' intersect B' intersect C') ?
    the third set of brackets should have C not C'
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