## Sets

# Operations on Sets

- Union of sets: A ∪ B = {x ∈ A or x ∈ B}
- Intersection of sets: A ∩ B = {x ∈ A and x ∈ B}
- Difference of sets: A – B = {x ∈ A and x ∉ B}
- Symmetric difference: A Δ B = (A – B) ∪ (B – A) [or] (A ∪ B) – (A ∩ B)
- Disjoint sets: A ∩ B = φ.
- A – B ⊆ A and B – A ⊆ B.

### View the Topic in this video From 38:06 To 48:48

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1. (i). **Idempotent Law**

a) A ∪ A = A

b) A ∩ A = A

(ii).** Identity Law**

a) A ∪ φ = A

b) A ∩ U = A

(iii). **Commutative Law**

a) A ∪ B = B ∪ A

b) A ∩ B = B ∩ A

(iv). **Associative Law**

a) (A ∪ B) ∪ C = A ∪ (B ∪ C)

b) A ∩ (B ∩ C) = (A ∩ B) ∩ C

(v). **Distributive Law**

a) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

b) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

2. a) A − (B ∩ C) = (A − B ) ∪ (A − C)

b) A − (B ∪ C) = (A − B) ∩ (A − C)

3. a) (A − B) ∪ (B − A) = (A ∪ B) − (A ∩ B)

b) A ∩ (B − C) = (A ∩ B) − (A ∩ C)

c) A ∩ (B Δ C) = (A ∩ B) Δ (A ∩ C)

d) (A ∩ B) ∪ (A − B) = A

e) A ∪ (B − A) = (A ∪ B)