Question 1191781: Given that n(Universal set) = 100, n(A) = 80 and n(B) = 60, find
a.The least possible value of n(A ∩ B),
b.The least possible value of n(A U B) and hence the greatest possible value of n[(A U B)'].
Answer by ikleyn(52833)   (Show Source):
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Given that n(Universal set) = 100, n(A) = 80 and n(B) = 60, find
a.The least possible value of n(A ∩ B),
b.The least possible value of n(A U B) and hence the greatest possible value of n[(A U B)'].
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(a) n(A ∩ B) is minimal when n(A U B) is maximal.
The maximal value for n(A U B) is 100.
The minimum possible value of n(A ∩ B) is then
n(A ∩ B) = n(A) + n(B) - n(A U B) = 80 + 60 - 100 = 140-100 = 40.
ANSWER. The minimum possible value for n(A ∩ B) is 40.
(b) The least possible value for n(A U B) is 80, when the Set B is a sub-set in A.
Then n( ( (A U B)' ) has the value of 20, which is maximum possible value for n(( A U B)' ).
ANSWER. The maximum possible value for n( (A U B)' ) is 20.
Solved and explained.
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