Question

If A and B are two finite sets such that n(A) = 35, n(B) = 30 and n(U) = 50 , then the greatest and the least value of n(A U B) are​

Answer 1

Answer:Since, n (U) = 60, while n (A) + n (B) = 21 + 43 = 64 which is greater than n(U), which is not possible hence sets A and B must have some common elements. Now, we know that,

n (A∪B) = n (A) + n (B) - n (A∩B).

So, for the least value of n (A∪B), the value of n (A∩B) must be maximum and vice-versa.

Maximum value of n(A∩B) = n(A) = 21

and the minimum value of n(A∩B) = n(A) + n(B) - n (U) = 21 + 43 - 60 = 64 - 60 = 4.

so,  43≤n(A∪B)≤60.  

Thus, the greatest value of n (A∪B) = 60

and, the least value of n (A∪B) = 43.

Step-by-step explanation: