Discrete Mathematics is a branch of mathematics that deals with discrete structures, such as integers, graphs, and statements, rather than continuous objects. It is used to model and solve real-world problems in computer science, engineering, and other fields.
A relation R on a set S is a set of ordered pairs (a,b) where a and b are elements of S. It represents a connection or association between elements of the set S.
When a relation R is defined on a set S of at least four ordered pairs, it means that there are at least four elements in the set S and each element is related to at least one other element in the set. This helps to establish patterns and connections between the elements in the set.
Some examples of relations in Discrete Mathematics include the "less than" relation on the set of integers, the "divides" relation on the set of positive integers, and the "is a sibling of" relation on the set of people.
A relation R on a set S can be represented in different ways, such as a table, a graph, or a matrix. In a table, the relation is represented by listing the ordered pairs (a,b) where a and b are related elements in S. In a graph, the elements of S are represented as vertices, and the relation R is represented by connecting the vertices with edges. In a matrix, the rows and columns represent the elements of S, and the entries in the matrix indicate whether or not the elements are related.