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Math Help - Finding subsets based off of given sets

  1. #1
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    Finding subsets based off of given sets

    I am working on a homework assignment for school. I have come up with an answer, but I would just like to clarify what I have.

    Question: Which of the following are subsets of which?
    A = {n P: n is odd}
    B = {n p: n is prime}
    C = {4n + 3: n P}
    D = {x R: x^2 - 8x + 15 = 0}


    Answer:
    What I did before anything was factor set D, and came up with the answers {3,5}. After factoring out set D, I went ahead and plug in numbers that fit the criteria for each set. After plugging in number fitting the conditions for each set, I came up with the answer that D is a subset of A. D is a subset of B. C is a subset of A. Are these answers correct?
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  2. #2
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    Re: Finding subsets based off of given sets

    Quote Originally Posted by needhelp101 View Post
    I am working on a homework assignment for school. I have come up with an answer, but I would just like to clarify what I have.

    Question: Which of the following are subsets of which?
    A = {n P: n is odd}
    B = {n p: n is prime}
    C = {4n + 3: n P}
    D = {x R: x^2 - 8x + 15 = 0}


    Answer:
    What I did before anything was factor set D, and came up with the answers {3,5}. After factoring out set D, I went ahead and plug in numbers that fit the criteria for each set. After plugging in number fitting the conditions for each set, I came up with the answer that D is a subset of A. D is a subset of B. C is a subset of A. Are these answers correct?
    Look at this fact $4(3)+3=15\in C~\&~15\notin A$
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  3. #3
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    Re: Finding subsets based off of given sets

    Plato, are you assuming "P" is the set of prime numbers? It seems to me, especially seeing " B= \{n \in P: n is prime\}" that P is intended to be the set of positive integers and 15 certainly is an odd positive integer.

    needhelp101, yes, D= {3, 5} and those are positive numbers which are both odd and prime so D is a subset of both A and B. Any number of the form 4n+ 3 is odd but not necessarily prime so C is a subset of A but not B as you say. A is not a subset of B because there exist off numbers that are odd but not prime (9 for example). B is not a subset of A because there is a prime number (2) that is prime but not odd.
    Last edited by HallsofIvy; February 26th 2014 at 03:08 PM.
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    Re: Finding subsets based off of given sets

    Quote Originally Posted by HallsofIvy View Post
    Plato, are you assuming "P" is the set of prime numbers? It seems to me, especially seeing "$B= \{n \in P: \text{n is prime}\}$" that P is intended to be the set of positive integers and 15 certainly is an odd positive integer.
    That certainly is a more logical reading of the OP.

    This should serve as warning to all users the necessary to define all terms that may be miss-read in a post.
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  5. #5
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    Re: Finding subsets based off of given sets

    Shall we flip a coin? needhelp101, how about letting us know what "P" was intended to mean?
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  6. #6
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    Re: Finding subsets based off of given sets

    I do apologize for the misunderstanding which I have cause you both. I should have put in the post somewhere what each set I was dealing with. On that note, "P" is actually being represented as the set of all positive integers. My apologies, I do appreciate the help and quick replies from you all. Thank you for your help
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