This chapter is divided into four sections, namely, Relations, Types of Relations, Functions, and Types of Functions.
Section 1: Relations In this section, you will learn about the concept of relations, types of relations, and the representation of relations through different methods such as arrow diagrams, ordered pairs, and graphs.
Section 2: Types of Relations In this section, you will learn about different types of relations such as reflexive, symmetric, transitive, and equivalence relations. You will also study the properties of each type of relation in detail.
Section 3: Functions In this section, you will learn about the concept of functions, types of functions, and their representation. You will also learn how to check whether a given relation is a function or not.
Section 4: Types of Functions In this section, you will learn about different types of functions such as one-to-one, onto, and inverse functions. You will also study the properties of each type of function in detail.
Relations: A relation is a set of ordered pairs. It defines the relationship between two sets of elements. For example, a relation can be established between the set of all students in a school and their corresponding roll numbers.
Types of Relations: There are various types of relations such as reflexive, symmetric, transitive, and equivalence relations. Reflexive relations have the property that every element in the set is related to itself. Symmetric relations have the property that if (a,b) is related, then (b,a) is also related. Transitive relations have the property that if (a,b) and (b,c) are related, then (a,c) is also related. Equivalence relations are reflexive, symmetric, and transitive.
Functions: A function is a special type of relation where each element in the domain has only one corresponding element in the range. In other words, for each value of x in the domain, there is only one value of y in the range. Functions are denoted by f(x).
Types of Functions: There are various types of functions such as one-to-one, onto, and inverse functions. One-to-one functions have the property that each element in the range corresponds to only one element in the domain. Onto functions have the property that every element in the range has at least one corresponding element in the domain. Inverse functions have the property that the inverse of a function f(x) is denoted by f^-1(x) and it satisfies f(f^-1(x)) = x and f^-1(f(x)) = x.
NUMERICAL WORKSHEET 2
NUMERICAL WORK SHEET 3
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