# Sets

A Set is the collection of objects called elements of the set. When we talk about sets, it is the most elementary building block used in mathematics. Once Sets are introduced  one can compare them, define operations similar to addition and multiplication on them and they can be used to define new objects such as various kinds of number systems and the elements belonging to different groups of Numbers. Most of the topics in modern analysis are based on the sets operations. We can say that sets are the collection of the objects selected from some universe called the universal set, which is largest among all sets. Sets are denoted by capital, bold letters or curly brackets. We can represent the sets by writing the elements of the sets in the curly braces separated by commas.
When we study Probability and sets together, then the probability of occurrence of any event from the given set forms probability sets. Probability set can be seen in the following example: Let’s have a set of Prime Numbers between 1 to 20. The set so formed will be P = 2, 3, 5, 7, 11, 13, 17. Now, we need to find the set probability of getting the product of any three randomly chosen numbers less than 31. We observe that only 3 numbers 2, 3, and 5 belong to this set as the product 2 * 3 * 5 = 30, which is less than 31. So we say the probability will be 3 / 7, where 7 is the total number of elements in the set of prime numbers below 20 and three numbers are there whose product is less than 31. As there are 3 numbers, so the number of ways these numbers can be arranged are factorial 3 = 3!= 3 * 2 * 1 = 6 ways.

## Law of Sets in Math

Sets in mathematics can be defined as a collection of well defined and distinct objects. The entities or objects contained by a Set are known as elements of set. We can represent Sets using capital letters. Example of Sets is A = {1, 2, 3, 4} where 'A' is the name of set and 1, 2, 3, and 4 are elements of set A. Now we will study Law of sets in Math.

## Subsets

A Set is a well defined collection of the object, where each object is called an element of the set. A set is always represented in capital letter like A, B, C, etc. The elements in the set are usually represented by small letters like x, y, z. So we say let set A contains the element 2, 4, 6, 8, 10. So it is written as A= 2, 4, 6, 8, 10. The elements of any set are represented ...Read More

## Power Sets

To understand power Sets, let us take a Set A = a, b, c.  We observe that this set ‘A’ has 3 elements, so three Subsets of the set ‘A’ can be a, b, and c. Moreover we can say that a set ‘A’ can also have a subset a, b, c which is called a proper subset of set ‘A’. Another important thing we must remember is null set, which is an empty subset of a set ‘A’. We conclude that if ...Read More

## Cardinality

Any Set ‘S’ which has ‘n’ different elements for some natural number ‘n’, then ‘n’ is called the cardinality of set ‘S’. It is also called as size of set ‘S’ and here ‘S’ is a finite set. If we have any set S = 1, 2, 3 in this set we have 3 elements, so the cardinality of set ‘S’ is 3. Word cardinality of Sets means the basic members in the family. Here the family of set con...Read More

## Special Sets

We say that the Sets of numbers which are used as the special names and symbols are called special sets. Some of the special sets are as follows:
1.     A Set of Natural Numbers: The set consisting of series of numbers 1, 2, 3, …..up to infinity  are called as special  set of  Natural numbers. It is represented by ‘N’.
2.     A set of whole numbers: The set consisting of ...Read More

## Types of Sets

A collection of different objects or we can say entities is known as Sets but these objects must be distinct and well defined. Sets is one of the most important concepts of mathematics from which different concepts of mathematics have been derived. The objects or entities which are included in a Set are also called elements of that set. Sets are basically denoted by capita...Read More