Question

Given that A and B are two disjoint subsets of a universal set U, with (n(U) = 15), (n(A) = 6), and (n(B) = 7), what is the cardinality of the union of A and B?

a) n(A ∪ B) = 6

b) n(A ∪ B) = 13

c) n(A ∪ B) = 13

d) n(A ∪ B) = 15

Answer 1

Final answer:
The cardinality of the union of sets A and B is 13.


Step-by-step explanation:
The cardinality of the union of sets A and B can be found by adding the number of elements in A and the number of elements in B, and subtracting the number of elements that they have in common.
In this case, n(A) = 6 and n(B) = 7. Since A and B are disjoint, their intersection (A ∩ B) is empty, so n(A ∪ B) = n(A) + n(B) = 6 + 7 = 13.
Therefore, the correct answer is option c) n(A ∪ B) = 13.