# Venn Diagram and sets

• Mar 21st 2010, 04:28 AM
jvignacio
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.
• Mar 21st 2010, 04:57 AM
Quote:

Originally Posted by jvignacio
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)}
• Mar 21st 2010, 05:15 AM
jvignacio
Quote:

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 :)
• Mar 21st 2010, 06:13 AM
Soroban
Hello, jvignacio!

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

Quote:

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.