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Math Help - Sets

  1. #1
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    Mar 2009
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    Sets

    Here is the problem
    Give examples of three sets

    1.A (subset) B (proper subset) c
    2. Ais in B, B is in C and A is not a part of C
    3. Ais in B and A (propersubset) C

    My answers
    1. A= {0,1,2} B=(-1,{0,1,2}, 3} c= {-1,3}
    2.A = {1} B= {{1},2,3} c= ?
    3. A= {1,2,3} B= {0,1,2,3,4} C= {{1,2},4}

    any help?are they right? wrong? where am i confused? any help thanks
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Dec 2008
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    South Coast of England
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    Hello j5sawicki
    Quote Originally Posted by j5sawicki View Post
    Here is the problem
    Give examples of three sets

    1.A (subset) B (proper subset) c
    2. Ais in B, B is in C and A is not a part of C
    3. Ais in B and A (propersubset) C

    My answers
    1. A= {0,1,2} B=(-1,{0,1,2}, 3} c= {-1,3}
    2.A = {1} B= {{1},2,3} c= ?
    3. A= {1,2,3} B= {0,1,2,3,4} C= {{1,2},4}

    any help?are they right? wrong? where am i confused? any help thanks
    You haven't made the questions clear. What, for example, does 'A is not a part of C' mean?

    However, #1 looks clear enough, and your answer is incorrect. If A \subseteq B, then you don't need the inner brackets inside set B. You can just say B = \{-1, 0, 1, 2, 3\}.

    And if B \subset C, then C needs to contain all the elements that are in B, plus at least one other. You have this the wrong way round; you have C \subset B.


    For #2, I assume you mean A \in B and B\in C, but I don't know (as I've said) what 'not a part of' means.

    If A \in B, and A is itself a set, then your first answer is correct: A=\{1\}, B =\{\{1\},2,3\}. But it would be better if you didn't mix sets with integers in set B. So B = \{\{1\},\{2\},\{3\}\} would probably be a better answer.

    If B \in C, then C must be a set containing sets like B as elements - and include B itself. For instance you could have C = \{\{\{1\},\{2\},\{3\}\}, \{\{1\},\{2\}\}\}


    For #3, you could have A and B the same as in #2, and then if A\subset C,\, C must contain all the elements in A, plus at least one more; for example, C = \{1, 2\}

    Grandad
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