NCERT Exemplar Solutions
Class 12 - Mathematics - Chapter 1: RELATIONS AND FUNCTIONS

True or False

Let R = {(3,1), (1,3), (3,3)} be a relation defined on the set A = {1,2,3}. Then R is symmetric, transitive but not reflexive.

Let f : \(\mathbb{R} \to \mathbb{R}\) be the function defined by f(x) = sin(3x + 2) for all x ∈ \(\mathbb{R}\). Then f is invertible.

Every relation which is symmetric and transitive is also reflexive.

An integer m is said to be related to another integer n if m is an integral multiple of n. This relation in \(\mathbb{Z}\) is reflexive, symmetric and transitive.

Let A = {0, 1} and N be the set of natural numbers. Then the mapping f : N → A defined by f(2n − 1) = 0 and f(2n) = 1 for all n ∈ N is onto.

The relation R on the set A = {1, 2, 3} defined as R = {(1,1), (1,2), (2,1), (3,3)} is reflexive, symmetric and transitive.

The composition of functions is commutative.

The composition of functions is associative.

Every function is invertible.

A binary operation on a set has always the identity element.