Properties of Set Union Operations with Proofs

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

The reader should have prior knowledge of the complement of a set. Click Here.

Properties of set Union:

1) A U A = A

Proof:

It is enough to show A U A ⊆ A and A ⊆ A U A

If X ⊆ Y and Y ⊆ X, then X = Y

Take A U A

x ∈ AUA

x ∈ A or x ∈ A

x ∈ A

A U A ⊆ A

Take A

x ∈ A

x ∈ A or x ∈ A

x ∈ AUA

A ⊆ A U A

2) AU Φ = A

3) A ∪ U = U

4) A ∪ A’ = U

5) A ⊆ A ∪ B and B ⊆ A ∪ B

6) A ∪ B = B ∪ A

7) A ∪ (B ∪ C) = (A ∪ B) ∪ C