SOLUTION: 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

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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(52834)   (Show Source): You can put this solution on YOUR website!
.
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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