Question

If n(A - B) = 18, n(AuB) = 70 and n(AnB) = 25, then find n(B)

Answer 1

n(B) = 26.

Explanation:

n(A U B) = 70 means there are a total number of elements in the 2 sets A and B.

n(AnB) = 25 means that 25 of the 70 elements are in Both sets A and Set B.

n(A - B) = 18 means the difference in number of elements in A and B is 18.

So we have

a - b = 18

a + b = 70 where a and b are the number of elements in and A and B. ( i. e. in n(A) and n(B) )

Adding the 2 equations

2a = 88

a = 44

and b = 70 - 44

= 26.