"Union and intersection of finite sets"

Sets

• Definition
  • A set is a collection of distinct objects, considered as an object in its own right. Objects in a set are called elements or members.

Union of Sets

• Union Definition

  • The union of two sets is written as L \cup G. It represents the set of all elements that are a member of either set L or set G, or both.

• Example

  • Given sets:
  • L = {a, b, g}
  • G = {a, e, k}
  • The union is:
  • L \cup G = {a, b, g} \cup {a, e, k} = {a, b, e, g, k}

Intersection of Sets

• Intersection Definition

  • The intersection of two sets is denoted as L \cap G. It consists of all the elements that are common to both set L and set G.

• Example

  • With the same sets above:
  • L = {a, b, g}
  • G = {a, e, k}
  • The intersection is:
  • L \cap G = {a, b, g} \cap {a, e, k} = {a}

Summary of Concepts

• Union: Combines all elements from both sets while eliminating duplicates.

• Intersection: Includes only those elements present in both sets.

• Important to express answers in roster form or set-builder notation where necessary.