A collection of objects is called a set. The number of elements in every set leads to their classification into different types. Therefore, you can say a set is a collection of dissimilar elements of the same kind. The following are the types of sets:-

• Singleton Set

A set with only one element present is called a singleton set. For example, Set Y = (4) is a singleton set. 

• Null Set

When the set is empty, or it doesn’t have any elements, it is called a null or void set. It is represented by {} or ϕ.

For example A = (x:x is a leap year between 2000 and 2004)

Between 2000 and 2004, we cannot find any leap year so, A = ϕ

• Proper Set

When a set consisting of some elements from the original is considered a proper subset; when a set contains original elements, along with the null set, it is called an improper subset.

• Finite Set

When in a set, the number of elements is finite, it is called a finite set. All the empty sets come under this category. In other words, a collection of no, or a constant number of elements is known as a finite set. For example:

C= ( x : x in a month in a year); Set C will have 12 elements.

D = (y : y is the zero of a polynomial (x4 – 6x2 + x + 2)); Set D will have 4 zeroes.

• Infinite Set

It is just the opposite of a finite set. When in a set, the number of elements is infinite, it is called an infinite set. For example:

D = (x : x is a natural number); There are infinite natural numbers. Thus, Set D is an infinite set.

E = (y : y is the ordinate of a point on a given line); Here, you can see there are infinite points on a line. So, E is an infinite set.

• Universal Set

Every set is formed based on the universal set and, as per the context, the Universal set is ascertained. Subsets of Universal sets are all the other sets, represented by U.

For example:-

The universal set of integers, rational numbers, and irrational numbers is the set of real numbers.

• Equal Set

Two sets C and D will be equal only when each element of set C is also the element of the set D. Even if they are subsets of each other, they will be called equal. It can be illustrated, as:

C = D 

C ⊂ D and D ⊂ C ⟺ C = D

If the condition is not met, which is mentioned above, the sets will be considered unequal. It can be shown as C ≠ D.

In mathematics, functions are considered a fundamental concept. It has various applications around the world. The set consisting of all possible values, regarded as inputs to a function, is called the domain of the function. The digit is positive, which is present under the square root bracket. To find out the range, you have to subtract the possible x-values to find the y-values. 

For example:

The domain of the function C is set B, i.e. (USA, Canada, UK, France)

A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

What are the sets and functions?

Answer.  Sets are the well-defined collection of different objects. Different mathematicians have defined it in different ways. The relationship of one variable with another is determined by function. In other words, it is a law or expression which is used to define a relationship.

What are the basic concepts of sets?

Answer. The main concept is that a set has elements, and both the sets may be termed as equal only if each set has the elements of the other set.

What are the types of sets?

Answer. The different type of sets are:

• Empty Set
• Singleton Set
• Finite Set
• Infinite Set
• Power Set
• Sub Set
• Universal Set

What are the four types of functions?

Answer. The following are the four types of functions :

• One – One function
• Many – one function
• Onto – function
• Into – function

What are the main functions of classification?

Answer. It assists in solving mathematical problems conveniently. Classification helps to allocate various objects in groups.