Sec 2.2 Question 8f) Prove the remaining parts of Theorem 2.2.2: Let U be the universe, and let A and B be subsets of U. Then A ∩ B = ∅ if and only if A ⊆ B c [Method 1: assume A ∩ B = ∅ then prove A...

Sec 2.2 Question 8f)

Prove the remaining parts of Theorem 2.2.2: Let U be the universe, and let A and B be subsets of U. Then

A ∩ B = ∅ if and only if A ⊆ B^c
[Method 1: assume A ∩ B = ∅ then prove A ⊆ B^c, and also assume A ⊆ B^c
then prove A ∩ B = ∅. Method 2: A ⊆ B^c
iff x ∈ A ⇒ x ∈ B^c
iff x ∈ A ⇒ x ∉ . . . iff (you should be able to show that no x in A is in B to obtain A ∩ B = ∅)]