Operations on Sets

Notations:-

∈ → belongs to

∉ → does not belongs to

⊆ → is a subset of

⊇ → is a superset of

⊂ → is a proper subset of

∀ → for all/ for every/ for each

∃ → there exists (at least one)

(i) Union of sets:-

Given ‘n’ sets n  2, then the set formed by taking all the elements of each of the n-sets as its element as its elements is called union of n-sets

The union of two sets A, B is denoted by A ∪ B and defined as A ∪ B = {x| x ϵ A V x ϵ B} or  

= {x| x ϵ at least one of sets A₁, A₂, --- A_n}

Note: - Every set is a subset of itself

(ii) Null set is subset of every set:-

A ⊆ A ∪ B, B ⊆ A ∪ B

If A, B are infinite disjoint sets |A ∪ B| = | A | + | B |

∪| A ∪ B | = ∩ (A) + ∪ (B)

In general,

N sets A₁, A₂, …, A_n are finite pair wise defined as 

Properties of union of sets:-

→ A ∪ A = A … {Idempotent law under union}

→ A ∪ B = B ∪ A ... {Commutative}

→ A ∪ B ∪ C = (A ∪ B) ∪ C = A ∪ (B ∪ C) … (associative)