A) \[{{2}^{9}}\] done clear
B) 6 done clear
C) 8 done clear
D) None of these done clear
View Solution play_arrowA) \[{{R}_{1}}=\{(x,\,y)|y=2+x,\,x\in X,\,y\in Y\}\] 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
View Solution play_arrowA) 4 done clear
B) 8 done clear
C) 64 done clear
D) None of these done clear
View Solution play_arrowA) {(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
View Solution play_arrowA) {(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
View Solution play_arrowA) 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
View Solution play_arrowA) Only symmetric done clear
B) Only transitive done clear
C) Only reflexive done clear
D) Equivalence relation done clear
View Solution play_arrowquestion_answer8) 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) Anti-symmetric done clear
View Solution play_arrowA) 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_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) None of these done clear
View Solution play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Anti-symmetric done clear
D) Transitive done clear
View Solution play_arrowA) Is from A to C done clear
B) Is from C to A done clear
C) Does not exist done clear
D) None of these done clear
View Solution play_arrowA) \[{{S}^{-1}}o{{R}^{-1}}\] done clear
B) \[{{R}^{-1}}o{{S}^{-1}}\] done clear
C) \[SoR\] done clear
D) \[RoS\] done clear
View Solution play_arrowA) {(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
View Solution play_arrowquestion_answer15) A relation from P to Q is
A) A universal set of P x Q done clear
B) P x Q done clear
C) An equivalent set of P x Q done clear
D) A subset of P x Q done clear
View Solution play_arrowA) A done clear
B) B done clear
C) A x B done clear
D) B x A done clear
View Solution play_arrowquestion_answer17) 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
View Solution play_arrowA) \[{{2}^{mn}}\] done clear
B) \[{{2}^{mn}}-1\] done clear
C) \[2mn\] done clear
D) \[{{m}^{n}}\] done clear
View Solution play_arrowA) \[m\ge n\] done clear
B) \[m\le n\] done clear
C) \[m=n\] done clear
D) None of these done clear
View Solution play_arrowA) {(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
View Solution play_arrowA) {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_arrowquestion_answer22) 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
View Solution play_arrowA) {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
View Solution play_arrowA) {(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_arrowA) {(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_arrowA) \[R\subset I\] done clear
B) \[I\subset R\] done clear
C) \[R=I\] done clear
D) None of these done clear
View Solution play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) An equivalence relation done clear
View Solution play_arrowA) Reflexive and symmetric done clear
B) Reflexive and transitive done clear
C) Symmetric and transitive done clear
D) Equivalence relation done clear
View Solution play_arrowquestion_answer29) 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
View Solution play_arrowquestion_answer30) 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_arrowquestion_answer31) 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 anti-symmetric done clear
View Solution play_arrowquestion_answer32) The relation "is subset of" on the power set P of a set A is
A) Symmetric done clear
B) Anti-symmetric done clear
C) Equivalency relation done clear
D) None of these done clear
View Solution play_arrowA) 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
View Solution play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) None of these done clear
View Solution play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) None of these done clear
View Solution play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) None of these done clear
View Solution play_arrowquestion_answer37) 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_arrowA) 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
View Solution play_arrowquestion_answer39) 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_arrowquestion_answer40) 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_arrowA) Symmetric and transitive done clear
B) Reflexive and symmetric done clear
C) A partial order relation done clear
D) An equivalence relation done clear
View Solution play_arrowA) 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_arrowquestion_answer43) 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_arrowquestion_answer44) Solution set of \[x\equiv 3\] (mod 7), \[p\in Z,\] is given by
A) {3} done clear
B) \[\{7p-3:p\in Z\}\] done clear
C) \[\{7p+3:p\in Z\}\] done clear
D) None of these done clear
View Solution 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 done clear
B) \[R\text{ }\cap \text{ }S\] is an equivalence relation on A done clear
C) \[R-S\] is an equivalence relation on A done clear
D) None of these done clear
View Solution 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 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_arrowA) {(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_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) None of these done clear
View Solution play_arrowA) Reflexive only done clear
B) Symmetric only done clear
C) Transitive only done clear
D) An equivalence relation done clear
View Solution play_arrowA) Reflexive done clear
B) Symmetric done clear
C) Transitive done clear
D) Equivalence done clear
View Solution play_arrowA) 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_arrowquestion_answer52) \[{{x}^{2}}=xy\] 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_arrowA) Reflexive done clear
B) Transitive done clear
C) Not symmetric done clear
D) A function done clear
View Solution play_arrowA) \[{{2}^{16}}\] done clear
B) \[{{2}^{12}}\] done clear
C) \[{{2}^{8}}\] done clear
D) \[{{2}^{4}}\] done clear
View Solution play_arrowA) 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_arrowA) \[{{2}^{9}}\] done clear
B) \[{{9}^{2}}\] done clear
C) \[{{3}^{2}}\] done clear
D) \[{{2}^{9-1}}\] done clear
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