Properties of Set Symmetric Difference

In this class, We discuss Properties of Set Symmetric Difference.

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

Properties of Set Symmetric Difference:

1) A + A = Φ

(A – A) ∪ (A – A)

Φ ∪ Φ = Φ

2) A + Φ = A

(A – Φ) ∪ (Φ – A)

A ∪ Φ = A

3) A + B = B + A

(A – B) ∪ (B – A)

(B – A) ∪ (A – B)

The above two statements are the same.

4) A+ B = (A ∪ B) – (A ∩ B)

The below diagram shows the proof.