Miscellaneous Exercise on Chapter 1
Jharkhand Board Mathematics Solutions for Exercise - Miscellaneous Exercise on Chapter 1
Simple step-by-step solutions to Miscellaneous Exercise on Chapter 1 questions of Relations and Functions from MATHEMATICS PART I : Class XII. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.
Questions from Miscellaneous Exercise on Chapter 1 with Hints & Solutions
Consider the binary operations : and : defined as and Show that is commutative but not associative, is associative but not commutative. Further, show that . [If it is so, we say that the operation distributes over the operation ]. Does distribute over ? Justify your answer.

Given a non‐empty set let : be defined as . Show that the empty set is the identity for the operation and all the elements of are invertible with .

Define a binary operation on the set as
Show that zero is the identity for this operation and each element of the set is invertible with being the inverse of

Let , and be functions defined by and . Are and equal? Justify your answer.

Let Then number of relations containing and which are reflexive and symmetric but not transitive is

Let Then number of equivalence relations containing is

Let be the Signum Function defined as
and if
and be the Greatest Integer Function given by , where is greatest integer less than or equal to . Then, does and coincide in ?

Number of binary operations on the set are
