A) \[{{2}^{9}}\]
B) 6
C) 8
D) None of these
View Answer play_arrowA) \[{{R}_{1}}=\{(x,\,y)|y=2+x,\,x\in X,\,y\in Y\}\]
B) \[{{R}_{2}}=\{(1,\,1),\,(2,\,1),\,(3,\,3),\,(4,\,3),\,(5,\,5)\}\]
C) \[{{R}_{3}}=\{(1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\}\]
D) \[{{R}_{4}}=\{(1,\,3),\,(2,\,5),\,(2,\,4),\,(7,\,9)\}\]
View Answer play_arrowA) 4
B) 8
C) 64
D) None of these
View Answer play_arrowA) {(1, 4, (2, 5), (3, 6),.....}
B) {(4, 1), (5, 2), (6, 3),.....}
C) {(1, 3), (2, 6), (3, 9),..}
D) None of these
View Answer play_arrowA) {(2, 1), (4, 2), (6, 3).....}
B) {(1, 2), (2, 4), (3, 6)....}
C) \[{{R}^{-1}}\] is not defined
D) None of these
View Answer play_arrowA) Reflexive but not symmetric
B) Reflexive but not transitive
C) Symmetric and Transitive
D) Neither symmetric nor transitive
View Answer play_arrowA) Only symmetric
B) Only transitive
C) Only reflexive
D) Equivalence relation
View Answer play_arrowquestion_answer8) Let \[P=\{(x,\,y)|{{x}^{2}}+{{y}^{2}}=1,\,x,\,y\in R\}\]. Then P is
A) Reflexive
B) Symmetric
C) Transitive
D) Anti-symmetric
View Answer play_arrowA) Less than n
B) Greater than or equal to n
C) Less than or equal to n
D) None of these
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) None of these
View Answer play_arrowA) Reflexive
B) Symmetric
C) Anti-symmetric
D) Transitive
View Answer play_arrowA) Is from A to C
B) Is from C to A
C) Does not exist
D) None of these
View Answer play_arrowA) \[{{S}^{-1}}o{{R}^{-1}}\]
B) \[{{R}^{-1}}o{{S}^{-1}}\]
C) \[SoR\]
D) \[RoS\]
View Answer play_arrowA) {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
B) {(3, 1) (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
C) {(3, 3), (3, 5), (5, 3), (5, 5)}
D) {(3, 3) (3, 4), (4, 5)}
View Answer play_arrowquestion_answer15) A relation from P to Q is
A) A universal set of P x Q
B) P x Q
C) An equivalent set of P x Q
D) A subset of P x Q
View Answer play_arrowA) A
B) B
C) A x B
D) B x A
View Answer play_arrowquestion_answer17) Let n = n. Then the number of all relations on A is
A) \[{{2}^{n}}\]
B) \[{{2}^{(n)!}}\]
C) \[{{2}^{{{n}^{2}}}}\]
D) None of these
View Answer play_arrowA) \[{{2}^{mn}}\]
B) \[{{2}^{mn}}-1\]
C) \[2mn\]
D) \[{{m}^{n}}\]
View Answer play_arrowA) \[m\ge n\]
B) \[m\le n\]
C) \[m=n\]
D) None of these
View Answer play_arrowA) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)}
B) {(2, 2), (3, 2), (4, 2), (2, 4)}
C) {(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)}
D) None of these
View Answer play_arrowA) {2, 3, 5}
B) {3, 5}
C) {2, 3, 4}
D) {2, 3, 4, 5}
View Answer play_arrowquestion_answer22) Let R be a relation on N defined by \[x+2y=8\]. The domain of R is
A) {2, 4, 8}
B) {2, 4, 6, 8}
C) {2, 4, 6}
D) {1, 2, 3, 4}
View Answer play_arrowA) {0, 1, 2}
B) {0, - 1, - 2}
C) {- 2, - 1, 0, 1, 2}
D) None of these
View Answer play_arrowA) {(8, 11), (10, 13)}
B) {(11, 18), (13, 10)}
C) {(10, 13), (8, 11)}
D) None of these
View Answer play_arrowA) {(3, 3), (3, 1), (5, 2)}
B) {(1, 3), (2, 5), (3, 3)}
C) {(1, 3), (5, 2)}
D) None of these
View Answer play_arrowA) \[R\subset I\]
B) \[I\subset R\]
C) \[R=I\]
D) None of these
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) An equivalence relation
View Answer play_arrowA) Reflexive and symmetric
B) Reflexive and transitive
C) Symmetric and transitive
D) Equivalence relation
View Answer play_arrowquestion_answer29) The relation R defined in N as \[aRb\Leftrightarrow b\] is divisible by a is
A) Reflexive but not symmetric
B) Symmetric but not transitive
C) Symmetric and transitive
D) None of these
View Answer play_arrowquestion_answer30) Let R be a relation on a set A such that \[R={{R}^{-1}}\], then R is
A) Reflexive
B) Symmetric
C) Transitive
D) None of these
View Answer play_arrowquestion_answer31) Let R = {(a, a)} be a relation on a set A. Then R is
A) Symmetric
B) Antisymmetric
C) Symmetric and antisymmetric
D) Neither symmetric nor anti-symmetric
View Answer play_arrowquestion_answer32) The relation "is subset of" on the power set P of a set A is
A) Symmetric
B) Anti-symmetric
C) Equivalency relation
D) None of these
View Answer play_arrowA) Every (a, b) \[\in R\]
B) No \[(a,\,b)\in R\]
C) No \[(a,\,b),\,a\ne b,\,\in R\]
D) None of these
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) None of these
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) None of these
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) None of these
View Answer play_arrowquestion_answer37) The void relation on a set A is
A) Reflexive
B) Symmetric and transitive
C) Reflexive and symmetric
D) Reflexive and transitive
View Answer play_arrowA) An equivalence relation on R
B) Reflexive, transitive but not symmetric
C) Symmetric, Transitive but not reflexive
D) Neither transitive not reflexive but symmetric
View Answer play_arrowquestion_answer39) Which one of the following relations on R is an equivalence relation
A) \[a\,{{R}_{1}}\,b\Leftrightarrow |a|=|b|\]
B) \[a{{R}_{2}}b\Leftrightarrow a\ge b\]
C) \[a{{R}_{3}}b\Leftrightarrow a\text{ divides }b\]
D) \[a{{R}_{4}}b\Leftrightarrow a<b\]
View Answer play_arrowquestion_answer40) If R is an equivalence relation on a set A, then \[{{R}^{-1}}\] is
A) Reflexive only
B) Symmetric but not transitive
C) Equivalence
D) None of these
View Answer play_arrowA) Symmetric and transitive
B) Reflexive and symmetric
C) A partial order relation
D) An equivalence relation
View Answer play_arrowA) Is reflexive
B) Is symmetric
C) Is transitive
D) Possesses all the above three properties
View Answer play_arrowquestion_answer43) The relation "congruence modulo m" is
A) Reflexive only
B) Transitive only
C) Symmetric only
D) An equivalence relation
View Answer play_arrowquestion_answer44) Solution set of \[x\equiv 3\] (mod 7), \[p\in Z,\] is given by
A) {3}
B) \[\{7p-3:p\in Z\}\]
C) \[\{7p+3:p\in Z\}\]
D) None of these
View Answer play_arrowquestion_answer45) 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
B) \[R\text{ }\cap \text{ }S\] is an equivalence relation on A
C) \[R-S\] is an equivalence relation on A
D) None of these
View Answer play_arrowquestion_answer46) 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
B) R and S are transitive, then \[R\text{ }\cap \text{ }S\] is also transitive
C) R and S are reflexive, then \[R\text{ }\cap \text{ }S\] is also reflexive
D) R and S are symmetric then \[R\text{ }\cup \text{ }S\] is also symmetric
View Answer play_arrowA) {(1, 3), (2, 2), (3, 2), (2, 1), (2, 3)}
B) {(3, 2), (1, 3)}
C) {(2, 3), (3, 2), (2, 2)}
D) {(2, 3), (3, 2)}
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) None of these
View Answer play_arrowA) Reflexive only
B) Symmetric only
C) Transitive only
D) An equivalence relation
View Answer play_arrowA) Reflexive
B) Symmetric
C) Transitive
D) Equivalence
View Answer play_arrowA) An equivalence relation
B) Reflexive and symmetric only
C) Reflexive and transitive only
D) Reflexive only
View Answer play_arrowquestion_answer52) \[{{x}^{2}}=xy\] is a relation which is [Orissa JEE 2005]
A) Symmetric
B) Reflexive
C) Transitive
D) None of these
View Answer play_arrowA) Reflexive
B) Transitive
C) Not symmetric
D) A function
View Answer play_arrowA) \[{{2}^{16}}\]
B) \[{{2}^{12}}\]
C) \[{{2}^{8}}\]
D) \[{{2}^{4}}\]
View Answer play_arrowA) Reflexive and symmetric but not transitive
B) Reflexive and transitive but not symmetric
C) Symmetric, transitive but not reflexive
D) Reflexive, transitive and symmetric
E) None of the above is true
View Answer play_arrowA) \[{{2}^{9}}\]
B) \[{{9}^{2}}\]
C) \[{{3}^{2}}\]
D) \[{{2}^{9-1}}\]
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