SOLUTION: A class of 30 music students includes 13 who play the piano, 16 who play the guitar, and 5 who play both piano and guitar. How many students in the class play neither instrument?

We will draw what is called a "Venn diagram":

Imagine you have all 30 students on a football field.

First draw a big rectangle to represent, say, the big football field, 
for all 30 music students to stand on.
 

 
Now on that football field draw a big circle for the 13 students
to stand in who play piano and label it P:
 

 
Next draw another big circle overlapping it for the 16 students
to stand in who play the guitar and label it G:
 

 
Now we tell the 5 students who like both both instruments to stand
in the overlapping part of those two circles.  So we'll write  
in there to represent the 5 students in that region.  Those 5 have to
stand in BOTH CIRCLES at the same time! The way to stand in both
circles at the same time is to stand in the overlapping part of the
circles:

 

and in the main drawing:
 

 
Since there are 13 students who play the piano, the rest of those 13 
besides the 5 that like both piano and guitar, that is, 13-5, or 8, 
will have to stand in this region, in which we write 8:
 
  
 
and in the main drawing:
 

 
Since there are 16 students who play guitar, the rest of those 16 
besides the 5 that like both, that is, 16-5, or 11, will have to 
stand in this region, in which we write 11:
 
`                      `  
 
and in the main drawing:
 

 
Now we have accounted for 8 + 5 + 11 or 24 of the 30 students.  That
leaves 30-24, or 6 students who play neither instrument, and so 
those 6 have to stand outside the two circles, like this:



So the answer is 6.
 
Edwin