Conclusion – Inverse Relation

In Conclusion, inverse relations are important in mathematics because they reveal reverse links between sets of elements. Their significance extends to a wide range of applications, including equation solving and function composition, cryptography, and data encryption.

Understanding inverse relations helps to appreciate the symmetric nature of relationships and their reversal, which improves knowledge of mathematical concepts and real-world events. Inverse linkages continue to play an important role in unraveling complicated interactions and operations, helping problem solving and analysis in a wide range of industries.

Inverse Relation

Inverse Relation: An inverse relation is the opposite of a given relation obtained by interchanging or swapping the elements of each ordered pair. In simple terms, if (x, y) is a point in a relation R, then (y, x) is an element in the inverse relation.

In this article, we will learn about Inverse Relation including their domain, range, and other properties as well.

Table of Content

  • What is an Inverse Relation?
    • Inverse Relation Meaning
  • Examples of Inverse Relation
  • Properties of Inverse Relations
  • Domain and Range of Inverse Relation
  • Inverse Relation Theorem
  • Inverse Relation Graph
  • Graphical Representation of Inverse Relation
  • Inverse Relation Solved Examples
  • Inverse Relation: Practice Problems

Similar Reads

What is an Inverse Relation?

Inverse relation refers to pairs of elements from two sets where the roles of the elements are reversed in each pair. In other words, if there is a relation between two elements in one set, the inverse relation involves switching the positions of those elements to form a new pair....

Examples of Inverse Relation

Some of the examples of inverse relations are:...

Properties of Inverse Relations

Inverse relations reverse the roles of the input and output values. The domain of a relation transforms into the range of its inverse, and vice versa. The composition of a relation with its inverse results in the identity relation i.e., R o (R-1) = Identity The inverse of an inverse relation is the original relation itself i.e., (R-1)-1 = R If a relation is injective (one-to-one), then its inverse is also injective. If a relation is surjective (onto), then its inverse is also surjective....

Domain and Range of Inverse Relation

In an ordered pair, the first element represents the “domain,” while the second element represents the “range” of a relation. Let me illustrate this using an example:...

Inverse Relation Theorem

Statement: The inverse relation theorem claims that for each relation R, (R⁻¹)⁻¹ = R....

Inverse Relation Graph

Inverse relations are represented graphically by drawing points and then reflecting them across the line y = x. Here are the steps:...

Graphical Representation of Inverse Relation

...

Inverse Relation Solved Examples

Example 1: Determine the inverse of the following relation. R = {(8, 9) (3, 5), (4, 6)}...

Inverse Relation: Practice Problems

Q1: Determine the domain and the range of the relation R = (x, x2), where x is a prime number smaller than 10. Q2: Determine the inverse of the function R = (x, x3), where x is a odd number smaller than 20. Q3: Determine the inverse of the following relation. R = {(15, 12), (18, 26), (24, 16)}...

Conclusion – Inverse Relation

In Conclusion, inverse relations are important in mathematics because they reveal reverse links between sets of elements. Their significance extends to a wide range of applications, including equation solving and function composition, cryptography, and data encryption....

Inverse Relation – FAQs

What is Meaning of Inverse Relation?...