need answer quickly.

Question

Let the Universal Set, S, have 156 elements. A and B are subsets of S. Set A contains 99 elements and Set B contains 25 elements. If the total number of elements in either A or B is 123, how many elements are in B but not in A?

Answer 1

a is the # of elements in A but NOT B, that is A ONLY

b is the # of elements in B but NOT A, that is B only

N is the # of elements in the INTERSECTION of A and B

a + N = 99

b + N = 25

a + b + N = 123

Subtracting the first two equations: a - b = 74

Subtracting the last two equations: -a = -98

a = 98

So then a - b = 74 and a = 98

98 - b = 74

-b = -24

b = 24

a = 98, b = 24 and a + b + N = 123

98 + 24 + N = 123

122 + N = 123

N = 1

98 are in A only

24 are in B only , which is the answer to the question

1 is in both A and B