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Math Help - difference between membership and subset operators

  1. #1
    Member Jskid's Avatar
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    difference between membership and subset operators

    I'm having difficulty understanding the difference between \in and \subset

    A question asks "true or false? \{1,2 \} \in \{1,2, \{ \{1,2 \} \} \} I thought this was true but it is false.
    Last edited by Jskid; December 6th 2011 at 11:27 PM.
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  2. #2
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    Re: difference between membership and subset operators

    1, 2, 1, 2 is not a set, so I don't know what you're referring to. Do you mean {1, 2} and {1, 2, 1, 2}? Those are sets, and they are the same set because they contain the same elements. They would also be subsets of each other.

    {1} is a subset of {1, 2}. 1 is a member of {1, 2}.
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  3. #3
    Member Jskid's Avatar
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    Re: difference between membership and subset operators

    Sorry the braces didn't show. No that's not what I meant.
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  4. #4
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    Re: difference between membership and subset operators

    Quote Originally Posted by Jskid View Post
    A question asks "true or false? \{1,2 \} \in \{1,2, \{ \{1,2 \} \} \} I thought this was true but it is false.
    For the set {1, 2} to be inside another set, you'd have to see {1, 2} or its equivalent inside that set.

    { {1, 2} } contains {1, 2}.
    {1, 2} does not contain {1, 2}. It is {1, 2}, however.

    {1, 2, {{1, 2}}} does not contain {1, 2}. It has three members. We just remove the outer braces to list them: 1, 2, and {{1, 2}}. Of these members, {{1, 2}} does indeed contain {1, 2}, but the enclosing set does not.

    Think of membership as "contains" and subset as "includes" and this might help.
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