A Set is a collection of distinct and defined elements. Sets are represented by using French braces {} with commas to separate the elements in a Set.

There are various types of sets as follows:
  • Finite Set
  • Infinite Set
  • Empty or Null Set
  • Equal Sets
  • Disjoint Sets
  • Intersecting Sets

Examples of Sets

  • The set of all points on a particular line.
  • The set of all lines in a particular plane.
  • A set can also contain elements which are themselves sets. For example, a set may contain 4, 5, {6, 7}.

There are three basic Set Operations.
  • Intersection of Sets
  • Union of Sets
  • Complement of Sets

Properties on Operations of Sets

A ⊂ B, B ⊂ C ⇒ A ⊂ C (Property of Transitivity)

A ⊂ B, B ⊂ A ⇒ A = B

A ∪ A = A

A ∩ A = ∅

A ∪ ∅ = A

A ∩ ∅ = ∅

A ∪ B = B ∪ A (Commutative law for addition)

A ∩ B = B ∩ A (Commutative law for multiplication)

(A ∪ B) ∪ C = A ∪ (B ∪ C) (Associative law for addition)

(A ∩ B) ∩ C = A ∩ (B ∩ C) (Associative law for multiplication)

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (Distributive law for addition)

A ∪ (B ∩ C) = (A ∩ B) ∪ (A ∩ C) (Distributive law for multiplication)