Matrix Representation of a Relation in Discrete Mathematics In Discrete Mathematics, relations can be represented in different ways such as ordered pairs, digraphs, and matrices. Among these, the matrix representation of a relation is very useful for performing operations like union, intersection, complement, and composition of relations. Matrix Representation of a Relation Let $A = \{a_1, a_2, a_3, \dots, a_n\}$ $B = \{b_1, b_2, b_3, \dots, b_m\}$ be two finite sets containing $n$ and $m$ elements respectively. Then the Cartesian product $A \times B$ contains $n \times m$ ordered pairs. Let $R$ be a relation from set $A$ to set $B$. Then, $$ R \subseteq A \times B $$ The matrix of relation $R$ , denoted by $M_R$, is an $n \times m$ matrix defined as follows: $$ M_R = [m_{ij}] $$ where $m_{ij} = 1$ if $(a_i, b_j) \in R$ $m_{ij} = 0$ if $(a_i, b_j) \notin R$ Question 1 Let $A = \{1,2,3,4\}$ $B = \{1,4,6,8,9,16\}$ A rel...
Types of Relations in Discrete Mathematics – Definitions, Examples & Solved Problems Relations are a fundamental concept in Discrete Mathematics and Graph Theory . They are widely used in equivalence relations, partial order relations, posets, lattices, and many real-life applications. Questions based on relations are frequently asked in GTU and engineering mathematics examinations . In this article, we explain the types of relations in a clear and exam-oriented manner with suitable examples and fully solved problems. Question 1 Explain types of a relation with a suitable example. Solution Definition of Relation Let A and B be two non-empty sets. A relation R from set A to set B is defined as a subset of the Cartesian product A × B . Mathematically, $$ R \subseteq A \times B $$ Types of Relations 1. Reflexive Relation A relation R on a set A is said to be reflexive if every element of A is related to itself. $$ (a,a) \in R \quad \text{for ...