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Math Help - Well-defined sets

  1. #1
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    Well-defined sets

    Hi! I tried to answer this question. Could you please tell me if I answered it correctly? I answered no, because we do not know exactly which persons are smokers, have a health problem, or is a male. Thank you.

    Let U = {xlx is an American}
    C = {xlx is a smoker}
    D = {xlx has a health problem}
    E = {xlx is a male}

    Are each of the sets C, D, and E well-defined? Explain.
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  2. #2
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    Quote Originally Posted by mathmagic View Post
    Let U = {xlx is an American}
    C = {xlx is a smoker}
    D = {xlx has a health problem}
    E = {xlx is a male}
    Are each of the sets C, D, and E well-defined? Explain.
    Look at this link.
    That is what I think of as well defined.
    Therefore, I think the answer to your question must come the textbook you are using.
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Plato View Post
    Look at this link.
    That is what I think of as well defined.
    Therefore, I think the answer to your question must come the textbook you are using.
    Can your link not be interpreted as the conditions for the sets must be absolutes? For example, \{x| x=1\} is well defined but \{x| x  \text{ counts on their computer}\} is not as "counts on their computer" can be taken in two ways.
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  4. #4
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    Quote Originally Posted by Swlabr View Post
    Can your link not be interpreted as the conditions for the sets must be absolutes? For example, \{x| x=1\} is well defined but \{x| x  \text{ counts on their computer}\} is not as "counts on their computer" can be taken in two ways.
    Well, I suppose it could. But that makes my point.
    The author of the textbook must have a particular idea of the level of rigor required to answer this question.
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  5. #5
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    In order that a set be well defined, we must be able, theoretically, to determine whether or not any given object is in the set. We could, certainly, given an specific person, test the DNA of that person to determine whether or not that person is male. Similarly, any given person either is or is not a smoker. Whether we know which or not is not relevant. I will concede that "health problem" might be sufficiently vague that the set might not be well defined.
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  6. #6
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    Thank you

    Great, thanks for all your help!
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