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Math Help - another set related question ...

  1. #1
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    another set related question ...

    Hi,

    I am trying to understand this set related question:

    ===========================
    Given the following sets:
    V = { n |0n 15}

    l = {3, 4, 5, 6, 7}

    and a list of 5 sets:

    Ai = { n V|n is a multiple of i}, where all i l
    (Notation: i {1,2,3} Ai = A1 A2 A3 )

    ilAi = ?
    ilAi = ?

    Answers:
    a. {11,13}
    b. {3,4,5,6,7,8,9,10,12,14,15}
    c. {0}
    d. {1,2}
    e. {0,3,4,5,6,7,8,9,10,12,14,15}
    f. {0,1,11,13}
    ===========================

    We need to determine what the answer is for:
    ilAi = ?
    ilAi = ?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: another set related question ...

    Use the given notation. You have to determine:
    \cap i \in I, A_i = ...
    and you know I=\{3,4,5,6,7\}
    so you have to determine:
    \cap i \in \{3,4,5,6,7 \}, A_i=A_3\cap ...
    Can you complete?
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  3. #3
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    Re: another set related question ...

    Quote Originally Posted by Siron View Post
    Use the given notation. You have to determine:
    \cap i \in I, A_i = ...
    and you know I=\{3,4,5,6,7\}
    so you have to determine:
    \cap i \in \{3,4,5,6,7 \}, A_i=A_3\cap ...
    Can you complete?
    No I can't ... don't really understand where you are going to ...
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  4. #4
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    Re: another set related question ...

    Quote Originally Posted by iwan1981 View Post
    No I can't ... don't really understand where you are going to ...
    @iwan1981
    Do you understand that A_3=\{0,3,6,9,12,15\}~\&~A_7=\{0,7,14\}~?.

    If you do tell us what A_4,~A_5,~\&~A_6 are.

    If you do not then short of doing the question for you, I don't know how we can help you.
    Last edited by Plato; July 10th 2011 at 03:52 AM.
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: another set related question ...

    @ Plato:
    Isn't 0 also a multiple? For example:
    A_3=\{0,3,6,9,12,15\}
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  6. #6
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    Re: another set related question ...

    Quote Originally Posted by Siron View Post
    @ Plato:
    Isn't 0 also a multiple of all sets? For example:
    A_3=\{0,3,6,9,12,15\}
    Frankly, I do not know.
    Do we consider 0 a multiple of 3? If so, then it should be there.
    It appears as if we should include it.
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  7. #7
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    Re: another set related question ...

    Quote Originally Posted by Plato View Post
    @iwan1981
    Do you understand that A_3=\{0,3,6,9,12,15\}~\&~A_7=\{0,7,14\}~?.

    If you do tell us what A_4,~A_5,~\&~A_6 are.

    If you do not then short of doing the question for you, I don't know how we can help you.

    A_4,~A_5,~\&~A_6

    A4 = {0, 4, 8, 12}
    A5 = {0, 5, 10, 15}
    A6 = {0, 6, 12}

    Right?
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  8. #8
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    Re: another set related question ...

    Quote Originally Posted by iwan1981 View Post
    A_4,~A_5,~\&~A_6
    A4 = {0, 4, 8, 12}
    A5 = {0, 5, 10, 15}
    A6 = {0, 6, 12}
    Right?
    Correct.
    Now
    \bigcap\limits_{i \in I} {A_i }  = A_3  \cap A_4  \cap A_5  \cap A_6  \cap A_7  = ?
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  9. #9
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    Re: another set related question ...

    Quote Originally Posted by Plato View Post
    Correct.
    Now
    \bigcap\limits_{i \in I} {A_i }  = A_3  \cap A_4  \cap A_5  \cap A_6  \cap A_7  = ?
    A3 = {0, 3, 6, 9, 12, 15}
    A4 = {0, 4, 8, 12}
    A5 = {0, 5, 10, 15}
    A6 = {0, 6, 12}
    A6 = {0, 7, 14}

    ∩ means means the set that contains all those elements that A1, A2, A3, A4, A5, A6 and A7 have in common so this will be: c. {0}

    Right?
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  10. #10
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    Re: another set related question ...

    Quote Originally Posted by iwan1981 View Post
    A3 = {0, 3, 6, 9, 12, 15}
    A4 = {0, 4, 8, 12}
    A5 = {0, 5, 10, 15}
    A6 = {0, 6, 12}
    A6 = {0, 7, 14}

    ∩ means means the set that contains all those elements that A1, A2, A3, A4, A5, A6 and A7 have in common so this will be: c. {0} Right?
    Good.
    Now what is the union?
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  11. #11
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    Re: another set related question ...

    Now what is the union?
    The Union = ∪

    ∪ means that the set of those elements which are either in A1 or in A2 or in A3 or in A4 or in A5 or in A6 or in A7 , or in all of them.

    So the Union is e. {0,3,4,5,6,7,8,9,10,12,14,15}

    right? :-)
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  12. #12
    MHF Contributor Siron's Avatar
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    Re: another set related question ...

    Correct!
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