**Algebra of Sets:**

**Idempotent**** Law****: **For any set A,

- A ∪ A = A
- A ∩ A = A

**Identity Law:** For any set A,

- A ∪ ϕ = A
- A ∩ U = A

**Commutative Law:** For any two sets A and B

- A ∪ B = B ∪ A
- A ∩ B = B ∩ A

**Associative Law:** For any three sets A, B and C

- ≤ A ∪ B) ∪ C = A ∪ ≤ B ∪ C)
- A ∩ ≤ B ∩ C) = ≤ A ∩ B) ∩ C

**Distributive Law: **For any three sets A, B and C

- A ∪ ≤ B ∩ C) = ≤ A ∪ B) ∩ ≤ A ∪ C)
- A ∩ ≤ B ∪ C) = ≤ A ∩ B) ∪ ≤ A ∩ C)

**De Morgan****’s Law: **For any two sets A and B

- ≤ A ∪ B)¢ = A¢ ∩ B¢
- ≤ A ∩ B)¢ = A¢ ∪ B¢

### POWER SET

The set of all subsets of a given set A is called the power set A and is denoted by P ≤ A). P ≤ A)* = *{S: S ⊆ A}

For example, if A *= *{1, 2, 3}, then

P≤ A) *= *{ ϕ,{1},{2},{3},{1},{1,2},{1,3},{2.3},{1,2,3}}

Clearly, if A has n elements, then its power set P≤ A) contains exactly 2^{n} elements.

**Some More Results:**

- n ≤ set of elements neither in A nor in B) = n ≤ A¢ ∩ B¢) = n≤ A ∪ B)¢ = n ≤ U) – n ≤ A ∪ B)
- n ≤ A¢ ∪ B¢) = n≤ A ∩ B)¢ = n ≤ U) – n ≤ A ∩ B)
- n ≤ A Δ B) = n [≤ A – B) ∪ ≤ B – A)] = n [≤ A ∩ B¢) ∪ ≤ A¢ ∩ B)] = n ≤ A) + n ≤ B) – 2n≤ A ∩ B).

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CBSE Class 11 Maths Sets Relations and Functions All Topic Notes CBSE Class 11 Maths All Chapters Notes

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