If A & B are subset of some universal set U with n(U)=50 n(A)=25 n(B)=32 & n((A U B)')=15 then n(A n B') equal

Question

a. 15
b. 25
c.35
d. 3
e. none

Answer 1

Answer is d. i.e. 3
n(A U B)') = 15 => n(A U B) = 50 - 15
Thus n(A U B) = 35

Definition of n(A n B') can be summarized as elements of A that belong to no other set but A.

So, Out of the n(A U B) = 35, 32 belong to B, which means that 3 belong to A and A alone.

Answer 2

In a two by two table with columns "A" and "not A" and rows "B" and "not B" you are given:

--- A A'
B w x
B' y z

you are given

n(U) = 50 ==> w + x + y + z = 50
n(A) = 25 ==> w + y = 25
[from which you can conclude x + z = 25]
n(B) = 32 ==> w + x = 32
[from which you can conclude y + z = 18]
n((A u B)') = 15 ==> z = 15
[from which you can conclude x = 10, y = 3, w = 22]

n(A and B') is y = 3.