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1. Let R = { (P,Q) : OP = OQ , O being the origin} be an equivalence relation on A . The equivalence class [( 1,2)] is
A. A
B. B
C. C
D. D
4. 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. Symmetric
B. Transitive
C. Reflexive
D. Equivalence relation
6. If A = {1,3,5,7} and define a relation, such that R = { (a,b) a,b A : |a+b| = 8}. Then how many elements are there in the relation R
A. 8
B. 16
C. 1
D. 4
7. In the set the relation R is defined by (a, b) R (c, d) ad = bc. Then R is
A. symmetric and transitive but not reflexive
B. reflexive and transitive but not symmetric
C. Equivalence relation
D. Partial order relation
9. Let R be the relation on the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3,3), (3,2)}. then R is
A. R is reflexive and symmetric but not transitive.
B. R is symmetric and transitive but not reflexive.
C. R is an equivalence relation.
D. R is reflexive and transitive but not symmetric.
10. Let A = {1,2,3,4,5,6,7}. P={1,2}, Q = {3, 7}. Write the elements of the set R so that P, Q and R form a partition that results in equivalence relation.
A. {4,5,6}
B. {0}
C. {1,2,3,4,5,6,7}
D. { }
11. Let R be a relation on set A of triangles in a plane. R = { (T1 , T2) : T1 , T2element ofA and T1 is congruent to T2} Then the relation R is______
A. Equivalence relation
B. Transitive
C. Symmetric
D. Reflexive
13. Let C = {(a, b): a2 + b2 = 1; a, b R} a relation on R, set of real numbers. Then C is
A. Equivalence relation
B. Reflexive
C. Transitive
D. Symmetric
14. Let A = {1,2,3,4} and B = { x,y,z}. Then R = {(1,x) , ( 2,z), (1,y), (3,x)} is
A. relation from B to A
B. Is not a relation
C. relation from A to B
D. relation from B to B
15. Let R be a relation on N, set of natural numbers such that m R n m divides n. Then R is
A. Reflexive and symmetric
B. Neither reflexive nor transitive
C. Reflexive and transitive
D. Symmetric and transitive
17. Let R be a relation on a finite set A having n elements. Then, the number of relations on A is
A. n x n
B. 2n
C. n2
D. 2nxn
18. Let R be a relation on N (set of natural numbers) such that (m, n) R (p, q)mq(n + p) = np(m + q). Then, R is
A. An Equivalence Relation
B. Only Reflexive
C. Symmetric and reflexive.
D. Only Transitive
19. 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}. Then, R is
A. Symmetric only
B. An equivalence relation
C. Reflexive and symmetric only
D. Reflexive and transitive only
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