Properties of Set Intersection Operation

In this class, We discuss the Properties of Set Intersection Operation.

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

1) A ∩ A = A

2) A ∩ U = A

3) A ∩ Φ = Φ

4) A ∩ B ⊆ A and A ∩ B ⊆ B

5) A ∩ B = B ∩ A

6) A ∩ (B ∩ C) = (A ∩ B)∩ C

Proof:

It is enough to show A ∩ (B ∩ C) ⊆ (A ∩ B)∩ C and (A ∩ B)∩ C ⊆ A ∩ (B ∩ C)

Let x ∈ (A ∩ B)∩ C

x ∈ (A ∩ B) and x ∈ C

x ∈ A and x ∈ B and x ∈ C

x ∈ A and x ∈ (B ∩ C)

x ∈ A ∩ (B ∩ C)

Similarly, we can show the opposite.