User:Kerry-Ann Downer

Introduction

Welcome to Wiki Bright Bloomers welcomes. This website was created to educate students about the different types of sets and the vocabulary that are used to describe them.

Are you aware that there are numerous types of sets?

CONTINUE FOR MORE!!!!!!!!

What is a Set?

A set is a collection of well-defined items or elements that do not change from one person to the next (BYJU'S, 2022).

Types of Sets

There are numerous types of sets. Finite, infinite, subset, universal, proper, singleton set are a few examples.


 * Finite Set

A finite set is a set with a countable number of items.

For example: A = {0, 3, 6, 9, …, 99}


 * Infinite Set

An infinite set is defined as a set where the number of items in the set cannot be counted and we cannot express it in Roster form.

For example: A set of all whole numbers, W= {0, 1, 2, 3, 4…}


 * Subset

A set Q is a subset of another set R if all elements of set Q are also elements of another set R.

For example: If Q is the set {2,4,6,8} and R is the {8,6,4,2}, then Q⊂R.


 * Proper Subset

The term "proper subset" means subset of but is not equal to.

If every member of X is an element of set Y and $|X| and $|Y|, set X is a proper subset of set Y and is written as X Y.

For example:  Let X = {1, 2, 3, 4, 5, 6} and Y = {1, 2} be the values for Y ⊂ X respectively. Because all elements in X are also contained in X and X has at least one element that is greater than set Y.


 * Universal Set

A universal set is one that includes all of the items of other sets, as well as its own. The letter 'U' is frequently used to represent it.

For example:   Assume Set A has all even numbers, such as 2, 4, 6, 8, 10, and Set B contains all odd numbers, such as 1, 3, 5, 7, 9, and so on. All-natural numbers are included in the universal set U, hence U = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.... As a result, all even and odd numbers are natural numbers, as we all know. As a result, Set U contains all of the items of Sets A and B.


 * Empty Set or Null Set

A set with no elements is called an empty set. It's denoted by the symbol ∅ or {}. An empty set is a finite set since it has a countable number of elements. The number of elements of an empty set, also known as a null set, is zero.

For example: S = {x | x ∈ N and 7 < x < 8} = ∅


 * Singleton Set / or Unit Set

A singleton set, also known as a unit set, has only one element. The letter S stands for a singleton set.

For example: S = {x | x ∈ N, 5 < x < 7} = {6}


 * Equal Set

Two sets are equal if they contain the same elements.

For example: If A = 3, 6, 9 and B = 9, 3, 6, they are equal since every element of set A is also an element of set B.


 * Set of Equivalents

Equivalent sets are those in which the number of elements of two sets are the same.

For example: If A = 1, 2, 6 and B = 16, 17, 22, they are equivalent since A's numbers of elements are equal to B's. In other words, |A| = |B| = 3


 * Overlapping Sets

When two sets A and B have at least one element in common, they are called overlapping sets.

For example: A= {a, b, c, d} and B= {a, e, i, o, u}


 * Disjoint Sets

If two sets A and B have no elements in common, they are said to be disjoint.

For example: Q = {x: x is a prime number} and R = {x: x is a composite number}.