A class of 50 music students includes 13 who play the piano

A class of 50 music students includes 13 who play the piano, 14 who play the guitar, and 8 who play both the piano and the guitar. How many students in the class play neither instrument? ___

Solution

n(A U B) = n(A) + n(B) - n(A B)
so students who play ateast one instrument is:
n(A U B)=13+14-8
n(A U B)=19
so students who donot play any instrument is:50-19=31