SET THEORY

SET THEORY

Objectives

What is a set?

Types of sets

Symbols used in set theory

What is a Set?

A set is a clearly defined collection of things that have something is common.

For example: Parishes of Jamaica- {St. Mary, St. James, Portland, ...}

A set is made up of members/elements. therefore all the parishes listed are call the ELEMENTS of the set.

Types of Sets

​Empty Set

Equivalent Set

Subset

Disjoint Set

Complement of a set

Intersection of a set

Union of a set

Equal Set

Equal sets have the same number of elements and exactly the same elements. The order in which they appear does not matter.

For example

A= {1, 2, 3, 4}

B= {4, 3, 2, 1}

Equivalent Set

An equivalent set is a set which has the same number of elements but the elements are not necessarily the same.

For example:

A= {1, 2, 3, 4}

B= {a, b, c, d}

Subset

A subset is a set contained in the given set. Every element of the subset is an element of the given set.

Disjoint Set

Disjoint sets have no common element

Complement of a set

The complement of a given set, is the set of all elements in its universal set that do not belong to the given set.

Intersection of a set

The intersection of two sets A and B, is the set of all elements common to both A and B.