Answer to Question #230195 in Discrete Mathematics for Ken

Question

What do universal set, S, have 91 elements. A and B are subsets of S. Set a contains 20 elements and CB contains 44 elements. If sets A and B have 6 elements in common, how many elements are in A but not in B?

Answer 1

From the diagram,

The universal set U=91 elements

Number of elements in A, n(A) = 20

Number of elements in B, n(B) = 44

Number of elements in A and B, n(AnB)=6

To get the number of elements in A but not in B which is denoted by n(AnB');

n(AnB') = n(A) - n(AnB)

= 20 - 6

= 14

Hence, 14 elements are in A but not in B.

(Shown in the diagram above).