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Friday, October 14, 2016

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  B = {x| x ϵ A V x ϵ B} or  
= {x| x ϵ at least one of sets A1, A2, --- An}

Note: - Every set is a subset of itself

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

⊆ 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, …, An 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)

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