Properties of Set Difference with Proofs

In this class, We discuss Properties of Set Difference with Proofs.

The reader should have prior knowledge of set theory basics. Click Here

Properties of set difference:

1) A – B = A ∩ B’

Let x ∈ A – B

x ∈ A and x ∉ B

x ∈ A and x ∈ B’

x ∈ A ∩ B’

2) A – A = Φ

3) A – Φ = A

4) A – B = B – A only if A = B

A = {1, 2, 5}

B = {1, 2, 5}

A – B = Φ and B – A = Φ

5) A – B = A if A ∩ B = Φ

6) A – B = Φ if A ⊆ B