Question

If cardinality of (AUB) = cardinality of A+ cardinality of B. This means: a) A is a subset of B b) B is a subset of A c) A and B are disjoint d) None of the mentioned

Answer 1

c

Explanation:

a) is wrong.

If A is a subset of B, then cardinality of (AUB) = cardinality B.

For example: A = {1}, B = {1,2,3} cardinality(A) = 1, cardinality(B) = 3.

AUB = {1,2,3} cardinality(AUB) = 3 = cardinality(B)

For the same reason as a), b) is wrong. If B is a subset of A, then the cardinality(AUB) = cardinality(A).

c) is right.

We have already seen that if a set A is a subset of a set B, then cardinality(AUB) = B.

Using A = {1} and B = {2,3}, cardinality(A) = 1, cardinality(B) = 2

Then AUB = {1,2,3} and cardinality(AUB) = 3 = cardinality(A)+cardinality(B)