Question

The cardinality of two disjoint sets A and B is in the ratio 2:1. If the cardinality of the union of these sets is 45, find the cardinality of the two sets.

Answer 1

Given n(A$\cup$B) = 45

n(A $\cap$ B) = 0

Let the cardinality of set B be x

n(A) = 2x

n(B) = x

n(A$\cup$ B) = n(A) + n(B) – n(A$\cap$B)

45 = 2x + x – 0

3x = 45

x = 15

Therefore n(A) = 2 $\times$ 15 = 30

n(B) = 15.