Miscellaneous Exercise on Chapter 1

Author:Jharkhand Board

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

EASY
12th Jharkhand Board
IMPORTANT

Consider the binary operations *: R×RR and o : R×RR defined as a*b=|a-b| and a o b=a,a,bR. Show that * is commutative but not associative, o is associative but not commutative. Further, show that a,b,cR,a*(b o c)=(a*b) o (a*c). [If it is so, we say that the operation * distributes over the operation o]. Does o distribute over *? Justify your answer.

HARD
12th Jharkhand Board
IMPORTANT

Given a non‐empty set X, let * : PX×PXPX be defined as A*B=(A-B)(B-A),A,BPX. Show that the empty set ϕ is the identity for the operation * and all the elements A of PX are invertible with A-1=A.

HARD
12th Jharkhand Board
IMPORTANT

Define a binary operation * on the set 0,1,2,3,4,5 as
a*b=a+bif a+b<6a+b-6if a+b6
Show that zero is the identity for this operation and each element a0 of the set is invertible with 6-a being the inverse of a.

EASY
12th Jharkhand Board
IMPORTANT

Let A=-1,0,1,2, B=-4,-2,0,2 and f, g:AB be functions defined by f(x)=x2-x,xA and gx=2x-12-1, xA. Are f and g equal? Justify your answer.

EASY
12th Jharkhand Board
IMPORTANT

Let A=1,2,3.Then number of relations containing 1,2 and 1,3 which are reflexive and symmetric but not transitive is

EASY
12th Jharkhand Board
IMPORTANT

Let A=1,2,3. Then number of equivalence relations containing 1,2 is

HARD
12th Jharkhand Board
IMPORTANT

Let f:RR be the Signum Function defined as
fx=1,x>0-1,x<0 and 0 if x=0
and g:RR be the Greatest Integer Function given by gx=x, where x is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1]?

EASY
12th Jharkhand Board
IMPORTANT

Number of binary operations on the set a,b are