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?
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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
Hence, 14 elements are in A but not in B.
(Shown in the diagram above).