# JEE Main & Advanced Mathematics Set Theory and Relations Question Bank

### done Relations

• A) ${{2}^{9}}$

B) 6

C) 8

D) None of these

• A) ${{R}_{1}}=\{(x,\,y)|y=2+x,\,x\in X,\,y\in Y\}$

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) ${{R}_{4}}=\{(1,\,3),\,(2,\,5),\,(2,\,4),\,(7,\,9)\}$

• A) 4

B) 8

C) 64

D) None of these

• A) {(1, 4, (2, 5), (3, 6),.....}

B) {(4, 1), (5, 2), (6, 3),.....}

C) {(1, 3), (2, 6), (3, 9),..}

D) None of these

• A) {(2, 1), (4, 2), (6, 3).....}

B) {(1, 2), (2, 4), (3, 6)....}

C) ${{R}^{-1}}$ is not defined

D) None of these

• A) Reflexive but not symmetric

B) Reflexive but not transitive

C) Symmetric and Transitive

D) Neither symmetric nor transitive

• A) Only symmetric

B) Only transitive

C) Only reflexive

D) Equivalence relation

• A) Reflexive

B) Symmetric

C) Transitive

D) Anti-symmetric

• A) Less than n

B) Greater than or equal to n

C) Less than or equal to n

D) None of these

• A) Reflexive

B) Symmetric

C) Transitive

D) None of these

• A) Reflexive

B) Symmetric

C)  Anti-symmetric

D) Transitive

• A) Is from A to C

B) Is from C to A

C) Does not exist

D) None of these

• A) ${{S}^{-1}}o{{R}^{-1}}$

B) ${{R}^{-1}}o{{S}^{-1}}$

C) $SoR$

D) $RoS$

• A) {(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)}

• 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

• A) A

B) B

C) A x B

D) B x A

• A) ${{2}^{n}}$

B) ${{2}^{(n)!}}$

C) ${{2}^{{{n}^{2}}}}$

D) None of these

• A) ${{2}^{mn}}$

B) ${{2}^{mn}}-1$

C) $2mn$

D) ${{m}^{n}}$

• A) $m\ge n$

B) $m\le n$

C) $m=n$

D) None of these

• A) {(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

• A) {2, 3, 5}

B) {3, 5}

C) {2, 3, 4}

D) {2, 3, 4, 5}

• A) {2, 4, 8}

B) {2, 4, 6, 8}

C) {2, 4, 6}

D) {1, 2, 3, 4}

• A) {0, 1, 2}

B) {0, - 1, - 2}

C) {- 2, - 1, 0, 1, 2}

D) None of these

• A) {(8, 11), (10, 13)}

B) {(11, 18), (13, 10)}

C) {(10, 13), (8, 11)}

D) None of these

• A) {(3, 3), (3, 1), (5, 2)}

B) {(1, 3), (2, 5), (3, 3)}

C) {(1, 3), (5, 2)}

D) None of these

• A) $R\subset I$

B) $I\subset R$

C) $R=I$

D) None of these

• A) Reflexive

B) Symmetric

C) Transitive

D) An equivalence relation

• A) Reflexive and symmetric

B) Reflexive and transitive

C) Symmetric and transitive

D) Equivalence relation

• A) Reflexive but not symmetric

B) Symmetric but not transitive

C) Symmetric and transitive

D) None of these

• A) Reflexive

B) Symmetric

C) Transitive

D) None of these

• A) Symmetric

B) Antisymmetric

C) Symmetric and antisymmetric

D) Neither symmetric nor anti-symmetric

• A) Symmetric

B) Anti-symmetric

C) Equivalency relation

D) None of these

• A) Every (a, b) $\in R$

B) No $(a,\,b)\in R$

C) No $(a,\,b),\,a\ne b,\,\in R$

D) None of these

• A) Reflexive

B) Symmetric

C) Transitive

D) None of these

• A) Reflexive

B) Symmetric

C) Transitive

D) None of these

• A) Reflexive

B) Symmetric

C) Transitive

D) None of these

• A) Reflexive

B) Symmetric and transitive

C) Reflexive and symmetric

D) Reflexive and transitive

• A) An equivalence relation on R

B) Reflexive, transitive but not symmetric

C) Symmetric, Transitive but not reflexive

D) Neither transitive not reflexive but symmetric

• 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) $a{{R}_{4}}b\Leftrightarrow a<b$

• A) Reflexive only

B) Symmetric but not transitive

C) Equivalence

D) None of these

• A) Symmetric and transitive

B) Reflexive and symmetric

C) A partial order relation

D) An equivalence relation

• A) Is reflexive

B) Is symmetric

C) Is transitive

D) Possesses all the above three properties

• A) Reflexive only

B) Transitive only

C) Symmetric only

D) An equivalence relation

• A) {3}

B) $\{7p-3:p\in Z\}$

C) $\{7p+3:p\in Z\}$

D) None of these

• 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

• 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

• A) {(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)}

• A) Reflexive

B) Symmetric

C) Transitive

D) None of these

• A) Reflexive only

B) Symmetric only

C) Transitive only

D) An equivalence relation

• A) Reflexive

B) Symmetric

C) Transitive

D) Equivalence

• A) An equivalence relation

B) Reflexive and symmetric only

C) Reflexive and transitive only

D) Reflexive only

• A) Symmetric

B) Reflexive

C) Transitive

D) None of these

• A) Reflexive

B) Transitive

C) Not symmetric

D) A function

• A) ${{2}^{16}}$

B) ${{2}^{12}}$

C) ${{2}^{8}}$

D) ${{2}^{4}}$

• A) 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

• A) ${{2}^{9}}$

B) ${{9}^{2}}$

C) ${{3}^{2}}$

D) ${{2}^{9-1}}$