Question

A universal set contains only sets A and B. If A∩B = Ø and A and B are not the empty set, then all of the following are true except
A and B are disjoint.
A is equal to B complement.
A∪B={}
A is not a subset of B.

Answer 1

The correct answer is:

A∪B={}

Explanation:

Since A∩B = ∅, we know that A and B have no elements in common. This means they are disjoint.

Since the universal set is made up of A and B, and A and B have no elements in common, then A is equal to the complement of B, or A = B'.

Since A and B have no elements in common, A is not a subset of B.

Since we are told at the beginning that A and B are not the empty set, there is no way that their union would be empty. The union of A and B, or A∪B, would contain at least two distinct elements, one from A and one from B.

Answer 2

The correct answer among the choices provided is the third option. All of the other statements are true except A∪B={}. Both A and B are said to be non-empty. The open and close parentheses is equal to an empty set.