The conversation between human and AI assistant.
How can you prove that if A ⊆ B, then A ∩ B' = ∅?
Can you explain how to prove that if A ⊆ B, then A ∩ B' = ∅?
Sure! We can prove this by contradiction. Assume that A ⊆ B and A ∩ B is not equal to the empty set. This means that there exists an element x that belongs to both A and B. But since A is a subset of B, it follows that x must also belong to A. This means that x belongs to both A and A', which is a contradiction. Therefore, A ∩ B must be equal to the empty set.