
Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is
A)
\[{{2}^{9}}\] done
clear
B)
6 done
clear
C)
8 done
clear
D)
None of these done
clear
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Let \[X=\{1,\,2,\,3,\,4,\,5\}\] and \[Y=\{1,\,3,\,5,\,7,\,9\}\]. Which of the following is/are relations from X to Y
A)
\[{{R}_{1}}=\{(x,\,y)y=2+x,\,x\in X,\,y\in Y\}\] done
clear
B)
\[{{R}_{2}}=\{(1,\,1),\,(2,\,1),\,(3,\,3),\,(4,\,3),\,(5,\,5)\}\] done
clear
C)
\[{{R}_{3}}=\{(1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\}\] done
clear
D)
\[{{R}_{4}}=\{(1,\,3),\,(2,\,5),\,(2,\,4),\,(7,\,9)\}\] done
clear
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Given two finite sets A and B such that n = 2, n = 3. Then total number of relations from A to B is
A)
4 done
clear
B)
8 done
clear
C)
64 done
clear
D)
None of these done
clear
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The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by
A)
{(1, 4, (2, 5), (3, 6),.....} done
clear
B)
{(4, 1), (5, 2), (6, 3),.....} done
clear
C)
{(1, 3), (2, 6), (3, 9),..} done
clear
D)
None of these done
clear
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The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then \[{{R}^{1}}\] is given by
A)
{(2, 1), (4, 2), (6, 3).....} done
clear
B)
{(1, 2), (2, 4), (3, 6)....} done
clear
C)
\[{{R}^{1}}\] is not defined done
clear
D)
None of these done
clear
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The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
A)
Reflexive but not symmetric done
clear
B)
Reflexive but not transitive done
clear
C)
Symmetric and Transitive done
clear
D)
Neither symmetric nor transitive done
clear
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The relation ?less than? in the set of natural numbers is [UPSEAT 1994, 98, 99; AMU 1999]
A)
Only symmetric done
clear
B)
Only transitive done
clear
C)
Only reflexive done
clear
D)
Equivalence relation done
clear
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Let \[P=\{(x,\,y){{x}^{2}}+{{y}^{2}}=1,\,x,\,y\in R\}\]. Then P is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
Antisymmetric done
clear
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Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is
A)
Less than n done
clear
B)
Greater than or equal to n done
clear
C)
Less than or equal to n done
clear
D)
None of these done
clear
View Solution play_arrow

For real numbers x and y, we write \[x\,R\,y\Leftrightarrow \] \[xy+\sqrt{2}\] is an irrational number. Then the relation R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
View Solution play_arrow

Let X be a family of sets and R be a relation on X defined by 'A is disjoint from B'. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Antisymmetric done
clear
D)
Transitive done
clear
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If R is a relation from a set A to a set B and S is a relation from B to a set C, then the relation SoR
A)
Is from A to C done
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B)
Is from C to A done
clear
C)
Does not exist done
clear
D)
None of these done
clear
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If \[R\subset A\times B\] and \[S\subset B\times C\,\] be two relations, then \[{{(SoR)}^{1}}=\]
A)
\[{{S}^{1}}o{{R}^{1}}\] done
clear
B)
\[{{R}^{1}}o{{S}^{1}}\] done
clear
C)
\[SoR\] done
clear
D)
\[RoS\] done
clear
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If R be a relation < from A = {1,2, 3, 4} to B = {1, 3, 5} i.e., \[(a,\,b)\in R\Leftrightarrow a<b,\] then \[Ro{{R}^{1}}\] is
A)
{(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)} done
clear
B)
{(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)} done
clear
C)
{(3, 3), (3, 5), (5, 3), (5, 5)} done
clear
D)
{(3, 3) (3, 4), (4, 5)} done
clear
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A relation from P to Q is
A)
A universal set of P × Q done
clear
B)
P × Q done
clear
C)
An equivalent set of P × Q done
clear
D)
A subset of P × Q done
clear
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Let A = {a, b, c} and B = {1, 2}. Consider a relation R defined from set A to set B. Then R is equal to set [Kurukshetra CEE 1995]
A)
A done
clear
B)
B done
clear
C)
A × B done
clear
D)
B × A done
clear
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Let n = n. Then the number of all relations on A is
A)
\[{{2}^{n}}\] done
clear
B)
\[{{2}^{(n)!}}\] done
clear
C)
\[{{2}^{{{n}^{2}}}}\] done
clear
D)
None of these done
clear
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If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
A)
\[{{2}^{mn}}\] done
clear
B)
\[{{2}^{mn}}1\] done
clear
C)
\[2mn\] done
clear
D)
\[{{m}^{n}}\] done
clear
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Let R be a reflexive relation on a finite set A having nelements, and let there be m ordered pairs in R. Then
A)
\[m\ge n\] done
clear
B)
\[m\le n\] done
clear
C)
\[m=n\] done
clear
D)
None of these done
clear
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The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : \[{{x}^{2}}{{y}^{2}}<16\}\] is given by
A)
{(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} done
clear
B)
{(2, 2), (3, 2), (4, 2), (2, 4)} done
clear
C)
{(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)} done
clear
D)
None of these done
clear
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A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by \[xRy\Leftrightarrow x\] is relatively prime to y. Then domain of R is
A)
{2, 3, 5} done
clear
B)
{3, 5} done
clear
C)
{2, 3, 4} done
clear
D)
{2, 3, 4, 5} done
clear
View Solution play_arrow

Let R be a relation on N defined by \[x+2y=8\]. The domain of R is
A)
{2, 4, 8} done
clear
B)
{2, 4, 6, 8} done
clear
C)
{2, 4, 6} done
clear
D)
{1, 2, 3, 4} done
clear
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If \[R=\{(x,\,y)x,\,y\in Z,\,{{x}^{2}}+{{y}^{2}}\le 4\}\] is a relation in Z, then domain of R is
A)
{0, 1, 2} done
clear
B)
{0,  1,  2} done
clear
C)
{ 2,  1, 0, 1, 2} done
clear
D)
None of these done
clear
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R is a relation from {11, 12, 13} to {8, 10, 12} defined by \[y=x3\]. Then \[{{R}^{1}}\] is
A)
{(8, 11), (10, 13)} done
clear
B)
{(11, 18), (13, 10)} done
clear
C)
{(10, 13), (8, 11)} done
clear
D)
None of these done
clear
View Solution play_arrow

Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by R ={(1, 3), (2, 5), (3, 3)}. Then \[{{R}^{1}}\] is
A)
{(3, 3), (3, 1), (5, 2)} done
clear
B)
{(1, 3), (2, 5), (3, 3)} done
clear
C)
{(1, 3), (5, 2)} done
clear
D)
None of these done
clear
View Solution play_arrow

Let R be a reflexive relation on a set A and I be the identity relation on A. Then
A)
\[R\subset I\] done
clear
B)
\[I\subset R\] done
clear
C)
\[R=I\] done
clear
D)
None of these done
clear
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Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)}. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
An equivalence relation done
clear
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An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is
A)
Reflexive and symmetric done
clear
B)
Reflexive and transitive done
clear
C)
Symmetric and transitive done
clear
D)
Equivalence relation done
clear
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The relation R defined in N as \[aRb\Leftrightarrow b\] is divisible by a is
A)
Reflexive but not symmetric done
clear
B)
Symmetric but not transitive done
clear
C)
Symmetric and transitive done
clear
D)
None of these done
clear
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Let R be a relation on a set A such that \[R={{R}^{1}}\], then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
View Solution play_arrow

Let R = {(a, a)} be a relation on a set A. Then R is
A)
Symmetric done
clear
B)
Antisymmetric done
clear
C)
Symmetric and antisymmetric done
clear
D)
Neither symmetric nor antisymmetric done
clear
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The relation "is subset of" on the power set P of a set A is
A)
Symmetric done
clear
B)
Antisymmetric done
clear
C)
Equivalency relation done
clear
D)
None of these done
clear
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The relation R defined on a set A is antisymmetric if \[(a,\,b)\in R\Rightarrow (b,\,a)\in R\] for
A)
Every (a, b) \[\in R\] done
clear
B)
No \[(a,\,b)\in R\] done
clear
C)
No \[(a,\,b),\,a\ne b,\,\in R\] done
clear
D)
None of these done
clear
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In the set A = {1, 2, 3, 4, 5}, a relation R is defined by R = {(x, y) x, y \[\in \] A and x < y}. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
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Let A be the nonvoid set of the children in a family. The relation 'x is a brother of y' on A is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
View Solution play_arrow

Let A = {1, 2, 3, 4} and let R= {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
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The void relation on a set A is
A)
Reflexive done
clear
B)
Symmetric and transitive done
clear
C)
Reflexive and symmetric done
clear
D)
Reflexive and transitive done
clear
View Solution play_arrow

Let \[{{R}_{1}}\] be a relation defined by \[{{R}_{1}}=\{(a,\,b)a\ge b,\,a,\,b\in R\}\]. Then \[{{R}_{1}}\] is [UPSEAT 1999]
A)
An equivalence relation on R done
clear
B)
Reflexive, transitive but not symmetric done
clear
C)
Symmetric, Transitive but not reflexive done
clear
D)
Neither transitive not reflexive but symmetric done
clear
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Which one of the following relations on R is an equivalence relation
A)
\[a\,{{R}_{1}}\,b\Leftrightarrow a=b\] done
clear
B)
\[a{{R}_{2}}b\Leftrightarrow a\ge b\] done
clear
C)
\[a{{R}_{3}}b\Leftrightarrow a\text{ divides }b\] done
clear
D)
\[a{{R}_{4}}b\Leftrightarrow a<b\] done
clear
View Solution play_arrow

If R is an equivalence relation on a set A, then \[{{R}^{1}}\] is
A)
Reflexive only done
clear
B)
Symmetric but not transitive done
clear
C)
Equivalence done
clear
D)
None of these done
clear
View Solution play_arrow

R is a relation over the set of real numbers and it is given by \[nm\ge 0\]. Then R is
A)
Symmetric and transitive done
clear
B)
Reflexive and symmetric done
clear
C)
A partial order relation done
clear
D)
An equivalence relation done
clear
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In order that a relation R defined on a nonempty set A is an equivalence relation, it is sufficient, if R [Karnataka CET 1990]
A)
Is reflexive done
clear
B)
Is symmetric done
clear
C)
Is transitive done
clear
D)
Possesses all the above three properties done
clear
View Solution play_arrow

The relation "congruence modulo m" is
A)
Reflexive only done
clear
B)
Transitive only done
clear
C)
Symmetric only done
clear
D)
An equivalence relation done
clear
View Solution play_arrow

Solution set of \[x\equiv 3\] (mod 7), \[p\in Z,\] is given by
A)
{3} done
clear
B)
\[\{7p3:p\in Z\}\] done
clear
C)
\[\{7p+3:p\in Z\}\] done
clear
D)
None of these done
clear
View Solution play_arrow

Let R and S be two equivalence relations on a set A. Then
A)
\[R\text{ }\cup \text{ }S\] is an equivalence relation on A done
clear
B)
\[R\text{ }\cap \text{ }S\] is an equivalence relation on A done
clear
C)
\[RS\] is an equivalence relation on A done
clear
D)
None of these done
clear
View Solution play_arrow

Let R and S be two relations on a set A. Then
A)
R and S are transitive, then \[R\text{ }\cup \text{ }S\] is also transitive done
clear
B)
R and S are transitive, then \[R\text{ }\cap \text{ }S\] is also transitive done
clear
C)
R and S are reflexive, then \[R\text{ }\cap \text{ }S\] is also reflexive done
clear
D)
R and S are symmetric then \[R\text{ }\cup \text{ }S\] is also symmetric done
clear
View Solution play_arrow

Let R = {(1, 3), (2, 2), (3, 2)} and S = {(2, 1), (3, 2), (2, 3)} be two relations on set A = {1, 2, 3}. Then RoS =
A)
{(1, 3), (2, 2), (3, 2), (2, 1), (2, 3)} done
clear
B)
{(3, 2), (1, 3)} done
clear
C)
{(2, 3), (3, 2), (2, 2)} done
clear
D)
{(2, 3), (3, 2)} done
clear
View Solution play_arrow

Let L denote the set of all straight lines in a plane. Let a relation R be defined by \[\alpha R\beta \Leftrightarrow \alpha \bot \beta ,\,\alpha ,\,\beta \in L\]. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
None of these done
clear
View Solution play_arrow

Let R be a relation over the set N × N and it is defined by \[(a,\,b)R(c,\,d)\Rightarrow a+d=b+c.\] Then R is
A)
Reflexive only done
clear
B)
Symmetric only done
clear
C)
Transitive only done
clear
D)
An equivalence relation done
clear
View Solution play_arrow

Let n be a fixed positive integer. Define a relation R on the set Z of integers by, \[aRb\Leftrightarrow nab\]. Then R is
A)
Reflexive done
clear
B)
Symmetric done
clear
C)
Transitive done
clear
D)
Equivalence done
clear
View Solution play_arrow

Let\[R=\{(3,\,3),\ (6,\ 6),\ (9,\,9),\ (12,\,12),\ (6,\,12),\ (3,\,9),(3,\,12),\,(3,\,6)\}\] be a relation on the set \[A=\{3,\,6,\,9,\,12\}\]. The relation is [AIEEE 2005]
A)
An equivalence relation done
clear
B)
Reflexive and symmetric only done
clear
C)
Reflexive and transitive only done
clear
D)
Reflexive only done
clear
View Solution play_arrow

\[{{x}^{2}}=xy\] is a relation which is [Orissa JEE 2005]
A)
Symmetric done
clear
B)
Reflexive done
clear
C)
Transitive done
clear
D)
None of these done
clear
View Solution play_arrow

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is [AIEEE 2004]
A)
Reflexive done
clear
B)
Transitive done
clear
C)
Not symmetric done
clear
D)
A function done
clear
View Solution play_arrow

The number of reflexive relations of a set with four elements is equal to [UPSEAT 2004]
A)
\[{{2}^{16}}\] done
clear
B)
\[{{2}^{12}}\] done
clear
C)
\[{{2}^{8}}\] done
clear
D)
\[{{2}^{4}}\] done
clear
View Solution play_arrow

Let S be the set of all real numbers. Then the relation R = {(a, b) : 1 + ab > 0} on S is [NDA 2003]
A)
Reflexive and symmetric but not transitive done
clear
B)
Reflexive and transitive but not symmetric done
clear
C)
Symmetric, transitive but not reflexive done
clear
D)
Reflexive, transitive and symmetric done
clear
E)
None of the above is true done
clear
View Solution play_arrow

If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is [NDA 2003]
A)
\[{{2}^{9}}\] done
clear
B)
\[{{9}^{2}}\] done
clear
C)
\[{{3}^{2}}\] done
clear
D)
\[{{2}^{91}}\] done
clear
View Solution play_arrow