Properties of Set Complement operation with Proof

In this class, We discuss Properties of Set Complement operation with Proof

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

1) A ∪ A’ = A

2) A ∩ A’ = Φ

3) U’ = Φ

4) Φ‘ = U

5) (A’)’ = A

6) (A ∪ B)’ = A’ ∩ B’ and (A ∩ B)’ = A’ ∪ B’

let x ∈ (A ∪ B)’

x ∉ (A ∪ B)

x ∉ A and x ∉ B

x ∈ A’ and x ∈ B’

x ∈ A’ ∩ B’

2) y ∈ (A ∩ B)’

y ∉ (A ∩ B)

y ∉ A or y ∉ B

y ∈ A’ or y ∈ B’

y ∈ A’ ∪ B’