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Math Help - Logical expression for set

  1. #1
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    Logical expression for set

    I don't know the logical expression for  \{x \in B|x \not \in C\}.

    I am thinking it could be one of these:

    \forall x(x \not \in c \rightarrow x \in B)

    or

    \forall x(x \in B \wedge x \not \in C)

    or
    <br />
\forall x \in B (x \not C)

    Could you help?
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  2. #2
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    {x in B | x not in C} is the set of all x such that x is in B and x is not in C.

    That is, for all x, we have x in {x in B | x not in C} if and only if (x is in B and x is not in C).

    Put another way, {x in B | x not in C} = B\C, where '\' stands for relative complement.
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  3. #3
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    Quote Originally Posted by novice View Post
    I don't know the logical expression for  \{x \in B|x \not \in C\}.
    \forall x(x \in B \wedge x \not \in C)
     \{x \in B|x \not \in C\}=B\setminus C.
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