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Math Help - empty set and intersection

  1. #1
    Member Jskid's Avatar
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    empty set and intersection

    Why is B \cap \{ \emptyset \} = \emptyset? Shouldn't it be B \cap \{ \emptyset \} = \{\emptyset \}?
    Last edited by mr fantastic; September 29th 2011 at 10:31 PM. Reason: Fixed latex.
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  2. #2
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    Re: empty set and intersection

    Quote Originally Posted by Jskid View Post
    Why is B \cap \{ \emptyset \} = \emptyset? Shouldn't it be B \cap \{ \emptyset \} = \{\emptyset \}?
    It can be either depending on whether \emptyset\in B.
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  3. #3
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    Re: empty set and intersection

    Quote Originally Posted by Jskid View Post
    Why is B \cap \{ \emptyset \} = \emptyset?
    B \cap \{ \emptyset \} = \emptyset is NOT a theorem. Who said it is?

    Quote Originally Posted by Jskid View Post
    Shouldn't it be B \cap \{ \emptyset \} = \{\emptyset \}?
    As emakarov alluded

    B \cap \{ \emptyset \} = \{\emptyset \} if and only if \emptyset\in B
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  4. #4
    Member Jskid's Avatar
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    Re: empty set and intersection

    First page of section 2.2 in Discrete Mathematics for Logic and Foundations.
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  5. #5
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    Re: empty set and intersection

    are you sure about the name of the book. amazon doesn't come up with any book with that name
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  6. #6
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    Re: empty set and intersection

    Quote Originally Posted by Jskid View Post
    First page of section 2.2 in Discrete Mathematics for Logic and Foundations.
    Then, if you're quoting the book correctly, taking you to mean that the book claims it's a theorem of ordinary set theory, then the book is in clear error.
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