Question

41. If n(u) = 500, n(A) = 150, n(B) = 300 and n(AB) = 70, then value of n(A-B) = ........
A. 300
B. 120
C. 360
D. 80
T

Answer 1

Answer:

Answer  D .   80

Step-by-step explanation:

Universal set U contains 500 ...as  n(U) = 500.

The sets A and B are part of the Universal set U. The are overlapping and have a non zero intersection.  

Cardinality of A = n (A) = 150

n (B) = 300

Given also the cardinality of the set of intersection of A and B:

  n( A ∩ B) = n (AB) = 70

We know that    the set  A - B = A -  A ∩ B

So    cardinality of  A - B = n(A) - n ( A∩ B)

ie.,    n (A - B) = 150 - 70

                         = 80

answer.

we can also find n (B - A )   =  n (B) - n( A ∩ B) = 300 - 70 = 230

we can find    n (A') = n(U) - n(A) = 350

   n (B') = n(U) - n(B) = 200

n (A U B) = n (A) + n(B) - n (A∩B) = 150 + 300 - 70 = 380

Answer 2

Step-by-step explanation:

A-B = A ∩ (¬ B)

The number of items in ...

A ... 150

A ∩ B ... 70

the elements in A ∩ (¬ B) are the elements of A after you remove the elements in A ∩ B, so subtract the two numbers to get the answer.