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Math Help - Sets

  1. #1
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    Sets

    Couple set questions..

    1.) Given:

    {x | x = k^2, k=1,2,3,...,100}, determine the cardinal #.

    I said it would be 100, as you'd have 100 numbers.

    2.) Suppose D is a proper subset of E;

    Determine the least possible # of elements that are in D.

    I'm assuming this is 1?

    3.) If D is a subset of E, are we able to say D is a proper subset of E?

    I'd say NO but my example I tried given contradicted itself.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DiscreteW View Post
    Couple set questions..

    1.) Given:

    {x | x = k^2, k=1,2,3,...,100}, determine the cardinal #.

    I said it would be 100, as you'd have 100 numbers.
    yes

    2.) Suppose D is a proper subset of E;

    Determine the least possible # of elements that are in D.

    I'm assuming this is 1?
    note that the empty set is a subset of any set, except perhaps the empty set ...now there's some food for thought

    3.) If D is a subset of E, are we able to say D is a proper subset of E?

    I'd say NO but my example I tried given contradicted itself.
    i wrote nonsense here, see my next post

    EDIT: see red
    Last edited by Jhevon; September 3rd 2008 at 08:20 PM.
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  3. #3
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    So um for 2 the least number would be nothing? The null set? Or 1? Or no possible answer?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DiscreteW View Post
    So um for 2 the least number would be nothing? The null set? Or 1? Or no possible answer?
    0 elements, since the empty set is a proper subset

    and for question 3, i read something incorrectly. the answer is still "no" though, but for a different reason. namely, a set is a subset of itself
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