Question 1191832: Two sets A and B are such that n(universal set) = 90, n(A) = 40 and n(B) = 68.Find
a.The smallest possible value of n(A U B),
b.The greatest possible value of n(A U B),
c.The greatest possible value of n(A n B').
Answer by ikleyn(52803)   (Show Source):
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Two sets A and B are such that n(universal set) = 90, n(A) = 40 and n(B) = 68.Find
a.The smallest possible value of n(A U B),
b.The greatest possible value of n(A U B),
c.The greatest possible value of n(A n B').
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(a) The smallest possible value of n(A U B) is 68, when the set A is a subset of the set B.
(b) The greatest possible value of n(A U B) is 90, when the sets A and B are maximally disjoint (= as disjoint as possible).
(c) n(B') = 90 - 68 = 22.
Therefore, the greatest possible value of n(A n B') is 40 + 22 = 62, when the sets A and B' are disjoint.
Solved. // All questions are answered.
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