Defining a Set – Elements of a Set A set is a group of items (in most cases) of the same kind. The items in a set are called the elements or members of a set. A set is well-defined when all its members can be listed. Examples of well-defined sets 1. A = the…

# Tag: Sets

## Finite and Infinite Sets

Finite and Infinite Sets A finite set is one in which it is possible to list and count all the members of the set. Example D = {days of the week} = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} And, n(D) = 7 An infinite set is one in which it is not possible to…

## Equal and Equivalent Sets

Equal and Equivalent Sets Two sets are equal if they both have the same members. Example If, F = {20, 60, 80} And, G = {80, 60, 20} Then, F=G, that is both sets are equal. Note: The order in which the members of a set are written does not matter. Two sets are equivalent…

## Empty Set

Empty Set An empty set is a set which has no members. Example If, H = {the number of dinosaurs on earth} Then, H is an empty set. That is, H = {} Note: An empty set is denoted by the symbol {}

## Subsets

Subsets A set N is a subset of a set X, if all the elements of N are contained in/members of the larger set X. Example If, X = {3, 5, 6, 8, 9, 10, 11, 13} And, N = {5, 11, 13} Then, N is a subset of X. That is, N ⊂ X…

## Universal Set

Universal Set This is the set from which all the elements being examined are members. The universal set is denoted by the symbol U. Example Using set builder notation, where {x:..} means ‘the set of all x such that’, If A = {0, 1, 2, 3, 4, 5, 6…} Then U = {x: x≥ 0,…

## Complement

Complement The complement of a set B, written B’, is the set of all the members of the universal set, which are not elements of the set B. Example If, U = {3, 5, 7, 9, 11, 13, 15, 17, 19} And, B = {5, 11, 17, 19} Then, B’ = {3, 7, 9, 13,…

## Intersection of Sets

Intersection of Sets The intersection of two sets is the listing of elements that are in both sets. The Venn diagram below shows A ∩ B, where ∩ means ‘intersect’. Example If, U = {2, 4, 6, 8, 10, 12, 14, 16} A = {4, 6, 8, 10, 12} B = {2, 10, 12, 14}…

## Union of Sets

Union of Sets The union of two sets A and B is the set of elements that are in A or B, or both. The Venn diagram below shows A ⋃ B. Example If, U = {2, 4, 6, 8, 10, 12, 14, 16} A = {4, 6, 8, 10, 12} B = {2, 10,…

## Number of Elements in named Subsets

Number of Elements in named Subsets When determining the number of elements in named subsets of two intersecting sets, given the number of elements in some of the other subsets, it is wise to firstly: – Decide what letters you will use to represent the subsets. – List the given information of elements. – Use…