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Math Help - Set Theory Question

  1. #1
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    Set Theory Question

    Hi,

    Just when I think I have my head wrapped around this stuff, I run into a wall. Here is my problem:

    If A∩B={1,3,5}, then B≠ { }

    Can someone tell me if this is true or false? If it is false I also need an explanation.

    My answer is False because { } is a subset of B which probably makes no sense.

    Any help is appreciated.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by nicole0714 View Post
    Hi,

    Just when I think I have my head wrapped around this stuff, I run into a wall. Here is my problem:

    If A∩B={1,3,5}, then B≠ { }

    Can someone tell me if this is true or false? If it is false I also need an explanation.

    My answer is False because { } is a subset of B which probably makes no sense.

    Any help is appreciated.
    of course it is true. if A \cap B = \{ 1,3,5 \} it means that 1,3, and 5 are elements of B. if B has elements, then it is not empty.
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  3. #3
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    Just by definition we know that
    3 \in A \cap B\quad  \Rightarrow \quad 3 \in A \wedge 3 \in B.
    The how can B be empty??
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