Let R be a relation on the set A of orde...

Let R be a relation on the set A of ordered pairs of positive integers defined by `(x , y) R (u , v)`if and only if `x v = y u`. Show that R is an equivalence relation.

Topper's Solved these Questions

RELATIONS AND FUNCTIONS
NCERT GUJARATI|Exercise EXERCISE 1.1|16 Videos
RELATIONS AND FUNCTIONS
NCERT GUJARATI|Exercise EXERCISE 1.2|12 Videos
PROBABILITY
NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|18 Videos
VECTOR ALGEBRA
NCERT GUJARATI|Exercise Miscellaneous Exercise on chapter 10|18 Videos

Similar Questions

Explore conceptually related problems

Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v) if and only if xv= yu. Show that R is an equivalence relation.

R is relation in N xxN as (a,b) R (c,d) hArr ad = bc . Show that R is an equivalence relation.

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

Let n be a fixed positive integer. Defiene a relation R in Z as follows : AA a, b in Z , aRb if and only if a - b divisible by n. Show that R is equivalance relation.

Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c on the set N xxN is an equivalence relation.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a , b)R a-b is divisible by ndot Show that R is an equivalence relation on Zdot

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Show that the relation R in the set A of all the books in a library of a college , given by R = {(x,y) : x and y have same number of pages} is an equivalence relation.

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

NCERT GUJARATI-RELATIONS AND FUNCTIONS -MISCLELLANEOUS EXERCISE ON CHAPTER 1

Let R be a relation on the set A of ordered pairs of positive integer...
Text Solution
|
Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...
Text Solution
|
Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...
Text Solution
|
If f:R to R is defined by f(x) = x^(2)-3x+2, write f{f(x)}.
Text Solution
|
Show that function f: R ->{x in R : -1 < x < 1}defined by f(x)=x/(1+...
Text Solution
|
Show that the function f: R->Rgiven by f(x)=x^3is injective.
Text Solution
|
Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...
Text Solution
|
Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...
Text Solution
|
Given a non-empty set X , consider P\ (X) which is the set of all subj...
Text Solution
|
Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...
Text Solution
|
Find the number of all onto functions from the set A={1,\ 2,\ 3,\ ...
Text Solution
|
Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...
Text Solution
|
Consider the binary operations *:" "RxxR ->R and o:" "R" "xx" "R->R de...
Text Solution
|
Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...
Text Solution
|
Define a binary operation *on the set {0," "1," "2," "3," "4," "5} as ...
Text Solution
|
Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...
Text Solution
|
LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...
Text Solution
|
Let A = {1, 2, 3}. Then number of equivalence relations containing (1...
Text Solution
|
Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...
Text Solution
|
Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...
Text Solution
|