MOUNT CARMEL PU COLLEGE – DEPT OF MATHEMATICS

RELATIONS AND FUNCTIONS

1. A relation R in a set A, if each element of A is related to every element of A, then R is
called
(a) Empty relation (b) Universal relation (c) trivial relation (d) none of these
2. Both the empty relation and the universal relation is
(a) Empty relation (b) trivial relation (c) universal relation (d) equivalence
3. Let A be the set of all students of boys school, then the relation R in A given by
R = {(a,b) : a is sister of b ) is
(a) Empty relation (b) symmetric relation (c) transitive relation (d) reflexive relation
4. A relation R in the set {1, 2, 3} given by R = {(1,1), (2,2), (3,3), (1,2), (1,3)}, then R is
(a) Reflexive, symmetric (b) reflexive, symmetric and transitive
(c)reflexive and transitive (d) reflexive but neither symmetric nor transitive
5. A relation R in the set A is called a reflexive relation, if
(a) (a,a) ∈ R, for all a ∈ A (b) (a,a) ∈ R, atleast one a ∈R
(c)if (a,b) ∈ R implies that (b,a) ∈ R, for all a, b ∈ A
(d) if (a,b) and (b,c) ∈ R implies that (a,c) ∈ R for all a, b, c ∈ A
6. A relation R in the set {1, 2, 3} given by R = {(1,2), (2,1)} is
(a) reflexive and symmetric (b) symmetric but not transitive
(c)symmetric and transitive (d) neither symmetric nor transitive
7. A relation R in the set {1, 2, 3} given by R = {(1,2), (2,1), (1,1)} is
(a) transitive but not symmetric (b) symmetric but not transitive
(c)symmetric and transitive (d) neither symmetric nor transitive
8. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1,2), (2,2), (1,1), (4,4), (1,3),
(3,3), (3,2)}. Choose the correct answer
(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation
9. Let R be the relation in the set N given by R = {(a,b) : a = b-2, b > 6}. Choose the
correct answer
(a) (2,4) R (b) (3,8) ∈ R (c) (6,8) ∈ R (d) (8,6) ∈ R
10. Consider the non-empty set consisting of children in a family and a relation R
defined as aRb if a is brother of b, then R is
(a) Symmetric but not transitive (b) transitive but not symmetric
(b) Neither symmetric nor transitive∈ (d) both symmetric and transitive
11. If a relation R on the set {1, 2, 3} be defined by R = {(1,2)} then R is
(a) reflexive (b) transitive (c) symmetric (d) none of these

Ms SWETHA S R
 MOUNT CARMEL PU COLLEGE – DEPT OF MATHEMATICS

12. Let L denote the set of all straight lines in a plane. Let a relation R be defined by
l R m if and only if l is perpendicular to m , for all l, m ∈ L, then R is
(a) Reflexive (b) symmetric (c) transitive (d) none of these
13. Let R be the relation in the set {1, 2, 3, 4} given by R = {(1,1), (2,2) (4,4), (3,3).
Choose the correct answer
(a) R is reflexive and symmetric but not transitive
(b) R is reflexive and transitive but not symmetric
(c) R is symmetric and transitive but not reflexive
(d) R is an equivalence relation
14. Let W denote the words in the English dictionary. Define the relation R by
R = {(x,y) ∈ W x W : the words x and y have atleast one letter in common}, then R is
(a) Not reflexive, symmetric and transitive (b)Reflexive, symmetric and not transitive
(b) Reflexive, symmetric and transitive (d) reflexive, not symmetric and transitive
1
15. Let f : R →R defined by f(x) = , x ∈ R, then f is
𝑥
(a) one one (b) onto (c) bijective (d) f is not defined
16. Let f : R →R defined by f(x) = 2x + 6 which is a bijective mapping , then f-1(x) is
𝑥
(a) − 3 (b) 2x + 6 (c) x – 3 (d) 6x + 2
2
17. If the set A contains 5 elements and the set B contains 6 elements, then the
number of one one and onto mappings from A to B is
(a) 720 (b) 120 (c) 0 (d) none of these
18. Let A = {1, 2, 3, ……n} and B = {a,b}, then the number of surjections from A to B is
(a) 𝑛𝑃2 (b) 2n – 2 (c) 2n – 1 (d) none of these
19. Let f : R →R defined by f(x) = 3x – 4 is invertible, then f-1(x) is
𝑥+4 𝑥
(a) (b) − 4 (c) 3x + 4 (d) none of these
3 3
20. Find the number of one one functions from A = {1, 2, 3} to itself is
(a) 8 (b) 4 (c) 6 (d) 3
21. Let f : {1, 2, 3} → {1, 2, 3}. Choose the correct answer
(a) If f is one one then f must be onto
(b) If is onto then f must be one one
(c) If f is one one then f is not onto
(d) Both A and B
22. Let f : R →R defined by f(x) = x4, x ∈ R , then f is
(a) one one but not onto (b) many one
(c) one one and onto (d) neither one one nor onto
23. Let f : R →R defined by f(x) = 3x, x ∈ R , then f is
(a) one one but not onto (b) many one
(c) one one and onto (d) neither one one nor onto

Ms SWETHA S R
 MOUNT CARMEL PU COLLEGE – DEPT OF MATHEMATICS

24. Let f : R →R defined by f(x) = x3, x ∈ R , then f is

(a) one one but not onto (b) many one
(c) one one and onto (d) neither one one nor onto
25. Let S = {1, 2, 3}, then the number of equivalence relations containing (1,2) is
(a) 1 (b) 2 (c) 3 (d) 4
26. Let S = {1, 2, 3}, then the number of equivalence relations containing (1,2) and
(2,1) is
(a) 1 (b) 2 (c) 3 (d) 4
27. Let S = {1, 2, 3} then the number of relations containing (1,2) and (1,3) which are
reflexive and symmetric but not transitive is
(a) 1 (b) 2 (c) 3 (d) 4
28.Let S ={a, b, c} and T = {1, 2, 3} then which of the following functions f from S to T ,
f-1 exists
(a) f = {(a,3), (b,2),(c,1) } (b) f = {(a,1), (b,1), (c,1)}
(c)f = {(a,2), (b,1), (c,1)} (d) f = {(a,1), (b,2), (c,1)}
29. If a relation R on the set {1, 2,3} be defined by R = {(1,1)} then R is
(a) symmetric but not transitive (b) transitive but not symmetric
(c) symmetric and transitive (d) neither symmetric nor transitive
30. The relation R in the set {1, 2, 3} given by R = {(1,1), (2,2), (1,2),(2,3), (3,3)} is
(a) reflexive (b) reflexive and transitive
(c) reflexive and symmetric (d) symmetric and transitive
31. Let A = {a, b, c} be a set defined on R = {(a,a), (b,b), (c,c)} is an example for
(a) symmetric (b) reflexive (c) transitive (d) equivalence
32. Let f : R →R defined by f(x) = x , x ∈ R , then f is
2

(a) one one but not onto (b) many one and onto
(c) one one and onto (d) neither one one nor onto
33. Let f : R →R defined by f(x) = |𝑥|, x ∈ R , then f is
(a) one one but not onto (b) onto but not one one
(c) one one and onto (d) neither one one nor onto
1
34. If f : 𝑅0 → 𝑅0 where 𝑅0 is non zero real numbers given by f(x) = , x ∈ R then f is
𝑥
(a) one one (b) onto (c) bijective (d) not defined
35. If the function f : N → N given by f(x) = 2x then f is
(a) one one but not onto (b) onto but not one one
(c) bijective (d) neither one one nor onto
36. Let f : R →R defined by f(x) = [x] then the function f is
(a) one one but not onto (b) one but not onto
(c) bijective (d) neither one one nor onto

Ms SWETHA S R
 MOUNT CARMEL PU COLLEGE – DEPT OF MATHEMATICS

37. Let f : R →R and g : R →R to be defined as f(x) = cosx and g(x) = 3x2 respectively then
fog(x) is
(a) 3cos2x (b) cos(3x2) (c) cos(2x3) (d)2cos3x
38. The function f : N → N is given by f(x) = 2x + 3, x ∈ N is
(a) surjective (b) injective (c) bijective (d) none of these
39. The function f : R → R is given by f(x) = 4x + 7, x ∈ R is
(a) one one (b) many one (c) odd (d) even
40. The relation R in the set {1, 2, 3} given by R= {(1,1), (2,3), (3,2), (3,3)} is
(a) symmetric only (b) symmetric and transitive
(c)transitive only (d) transitive but not symmetric
41. Statement 1: A relation R ={(1,1) ,(1,2) , (2,1)} defines on the set A = {1,2,3} is
transitive
Statement 2: A relation R on the set A is transitive if (a,b) and (b,c)∈ R then (a,c)∈R
(a) Statement 1 is true and Statement 2 is false
(b) Statement 1 is true and Statement 2 is true, statement 2 is correct explanation
for statement 1
(c ) Statement 1 is true and Statement 2 is true, statement 2 is not a correct
explanation for statement 1
(d ) Statement 1 is false and Statement 2 is true
42. Let f : {1,2,3} → {1,2,3} is a function
Statement 1: If f is one one then f must be onto
Statement 2: If f is onto then f must be one one
(a) Statement 1 is true and Statement 2 is false
(b) Statement 1 is true and Statement 2 is true
(c) Statement 1 is false and Statement 2 is false
(d) Statement 1 is false and Statement 2 is true
43. Statement 1:Let f : R → R defined by f(x) = 3x is bijective
Statement 2: A function f : A → B is a bijective function if f is one one and onto
(a) Statement 1 is true and Statement 2 is false
(b) Statement 1 is true and Statement 2 is true, Statement 2 is correct explanation
of statement 1
(c) Statement 1 is true and Statement 2 is true, Statement 2 is not correct
explanation of statement 1
(d) Statement 1 is false and Statement 2 is false
44. Assertion(A): In a set A = {1,2,3} a relation R defined as R = {(1,1), (2,2)} is
Reflexive
Reason(R): A relation R is reflexive in set A if (a,a) ∈ R for all a∈A
(a) A is false but R is true (b) A is true and R is false
(c) A is true and R is true (d) A is false and R is false
Ms SWETHA S R
 MOUNT CARMEL PU COLLEGE – DEPT OF MATHEMATICS

45. Assertion(A): In a set A = {1,2,3} a relation R defined as R = {(1,2)} is transitive

Reason(R): A singleton relation is transitive
(a) A is false but R is true (b) A is true and R is false
(c) A is true and R is true (d) A is false and R is false
46. Statement 1: A function f : A → B cannot be an onto function if n(A) < n(B)
Statement 2: A function f is onto if every element of co domain has atleast one
pre image in the domain
(a) Statement 1 is true and Statement 2 is false
(b) Statement 1 is true and Statement 2 is true, Statement 2 is correct explanation
of statement 1
(c) Statement 1 is true and Statement 2 is true, Statement 2 is not correct
explanation of statement 1
(d) Statement 1 is false and Statement 2 is false
47. If f: {2,8} → { -2, 2, 4} for the following figure f is

(a) f is one one but not onto

2 -2
(b) f is neither one one nor onto
2 (c) f is not a function
8 4 (d) f is not one one but onto

48. If f : R → R ,then graph of the function is

(a) f is one one but not onto

(b) f is one one and onto
(c) f is neither one one nor onto
(d) f is onto but not one one

49. If f : R → R ,then graph of the function is

(a) f is one one but not onto

(b) f is one one and onto
(c) f is neither one one nor onto
(d) f is onto but not one one

Ms SWETHA S R
 MOUNT CARMEL PU COLLEGE – DEPT OF MATHEMATICS

50. Given a set A = {1,2,3} and a relation R = {(3,1), (1,3), (3,3)}, the relation R will be
(a) reflexive if (1,1) is added (b) symmetric if (2,3) is added
(c) transitive if (1,1) is added (d) symmetric if (3,2) is added
51. Statement 1: If R and S are two equivalence relations on set A, then R ∩ S is also
an equivalence relation on set A
Statement 2: The union of two equivalence relations on a set is not necessarily
relation on the set.
Statement 3: The inverse of an equivalence relation is an equivalence relation
(a) All 3 statements are true
(b) All 3 statements are false
(c) 1 and 2 statements are true but 3 is false
(d) 1 and 3 statements are true but 2 is false

Ms SWETHA S R