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Math Help - Venn Diagram and sets

  1. #1
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    Venn Diagram and sets

    Hey guys having trouble with the practice problem.

    There are 20 students in an introductory music class. 9 students can play the piano and 4 students can play guitar. If 3 students can play both guitar and piano, then how many students can play neither instrument? justify answer by making some sets and cardinalitys.

    Would it be something like:

    Only Piano: {9}
    Only Guitar: {4}
    Guitar & Piano {3}, would i have to remove 2 from piano group and 1 from guitar group to get the final neither group? Bit confused!

    Thanks.
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    Hey guys having trouble with the practice problem.

    There are 20 students in an introductory music class. 9 students can play the piano and 4 students can play guitar. If 3 students can play both guitar and piano, then how many students can play neither instrument? justify answer by making some sets and cardinalitys.

    Would it be something like:

    Only Piano: {9}
    Only Guitar: {4}
    Guitar & Piano {3}, would i have to remove 2 from piano group and 1 from guitar group to get the final neither group? Bit confused!

    Thanks.
    Hi jvignacio,

    The students who play piano can be divided into two subsets,
    those that play only piano, and those that play both guitar and piano.

    Hence,

    Only piano: {9-3}
    Only guitar: (4-3}

    The total subsets then are....

    Only piano: {6}
    Only guitar: {1}
    Piano and guitar: {3}
    Neither: {20-(6+1+3)}
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    Hi jvignacio,

    The students who play piano can be divided into two subsets,
    those that play only piano, and those that play both guitar and piano.

    Hence,

    Only piano: {9-3}
    Only guitar: (4-3}

    The total subsets then are....

    Only piano: {6}
    Only guitar: {1}
    Piano and guitar: {3}
    Neither: {20-(6+1+3)}
    Thanks for that! now i understand! too easy
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  4. #4
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    Hello, jvignacio!

    Your title mentions a Venn diagram.
    Did you make one?


    There are 20 students in an introductory music class.
    9 students can play the piano and 4 students can play guitar.
    If 3 students can play both guitar and piano,
    then how many students can play neither instrument?
    Code:
          * - - - - - - - - - - - - - - - - - - - *
          |                                       |
          |       * - - - - - - - *               |
          |       | Piano only    |               |
          |       |     6         |               |
          |       |       * - - - + - - - *       |
          |       |       |  Both |       |       |
          |       |       |   3   |       |       |
          |       * - - - + - - - *       |       |
          |               |        1      |       |
          |               |   Guitar only |       |
          |      10       * - - - - - - - *       |
          |   Neither                             |
          * - - - - - - - - - - - - - - - - - - - *

    I hope you can see how the numbers are distributed.

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