Every function is a relation but every relation is not a(i) Closure property We say that * on S satisfies the closure9: B→ C, thenB anu6. Binary operation Let S be a non-empty set điu* ht ali Operation(y,xIf (X,Yf(x)gof : A C such that:(gof) (x) = g{f(x)},▼ x e AgofsymmeNotefunction.For exFor ton S such thatthenFor ea eS, b eS= a *b e1SVa,b eS.Then, * is called a binary operation on S.3x1oteHere, Aproperty, ifa e S, b eS= a* beS, Va, b eS.a) ForRi(ii) Commutative law OperationS is said to becommutative, ifa* b = b * a V a,b eS.on(iii) Associative law Operation * on S is said to be associative,if (a * b)* c = a * (b * c); a, b, c eS.(© Forz =pa(2,Exercise 1.1(iii) (a) FoQuestion 1.reflexive, symmetric and transitive :(i) Relation RR = {(x, y): 3x-y 0}(ii) RelationR = {(x, y): y = x + 5 and x < 4}(iii) Relation R in the set A={1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisibleby x}(iv) Relation R in the set Z of all integers defined as R = {(x, y): x -y is aninteger }Determine whether each of the following relations arein(b) Fthe set A= {1, 2, 3, ......,13, 14 } definedashonof natural(c)R.inset Nnumbersdefinedas(iv) (aob olnw awREDMI NOTE 5 PROMI DUAL CAMERA

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Exercise 1.1 Question 1. Determine whether each of the following ręlations are eflexive, symmetric and transitive : (i) Relation R = {(x, y): 3x-y 0} R in the set A= {1, 2, 3, ...13, 14} defined as ...... %3D R in honte N of natural numbers defined (ii) Relation R R = {(x, y): y = x + 5 and x < 4} iii) Relation R in the set A= {1, 2, 3, 4, 5, 6} as R= {(x, y): y is divisible by x} set as holla

Exercise 1.1 Question 1. Determine whether each of the following ręlations are eflexive, symmetric and transitive : (i) Relation R = {(x, y): 3x-y 0} R in the set A= {1, 2, 3, ...13, 14} defined as ...... %3D R in honte N of natural numbers defined (ii) Relation R R = {(x, y): y = x + 5 and x < 4} iii) Relation R in the set A= {1, 2, 3, 4, 5, 6} as R= {(x, y): y is divisible by x} set as holla

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Every function is a relation but every relation is not a
(i) Closure property We say that * on S satisfies the closure
9: B→ C, then
B anu
6. Binary operation Let S be a non-empty set điu* ht ali Operation
(y,x
If (X,Y
f(x)
gof : A C such that:
(gof) (x) = g{f(x)},▼ x e A
gof
symme
Note
function.
For ex
For t
on S such that
then
For e
a eS, b eS= a *b e1
SVa,b eS.
Then, * is called a binary operation on S.
3x1
ote
Here, A
property, if
a e S, b eS= a* beS, Va, b eS.
a) For
Ri
(ii) Commutative law Operation
S is said to be
commutative, if
a* b = b * a V a,b eS.
on
(iii) Associative law Operation * on S is said to be associative,
if (a * b)* c = a * (b * c); a, b, c eS.
(© For
z =
pa
(2,
Exercise 1.1
(iii) (a) Fo
Question 1.
reflexive, symmetric and transitive :
(i) Relation R
R = {(x, y): 3x-y 0}
(ii) Relation
R = {(x, y): y = x + 5 and x < 4}
(iii) Relation R in the set A={1, 2, 3, 4, 5, 6} as R = {(x, y): y is divisible
by x}
(iv) Relation R in the set Z of all integers defined as R = {(x, y): x -y is an
integer }
Determine whether each of the following relations are
in
(b) F
the set A= {1, 2, 3, ......,13, 14 } defined
as
hon
of natural
(c)
R.
in
set N
numbers
defined
as
(iv) (a
ob olnw aw
REDMI NOTE 5 PRO
MI DUAL CAMERA

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