MCQOPTIONS
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MCQOPTIONS
This section includes 657 Mcqs, each offering curated multiple-choice questions to sharpen your Testing Subject knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Consider the relation: R’ (x, y) if and only if x, y>0 over the set of non-zero rational numbers,then R’ is _________ |
| A. | not equivalence relation |
| B. | an equivalence relation |
| C. | transitive and asymmetry relation |
| D. | reflexive and antisymmetric relation |
| Answer» C. transitive and asymmetry relation | |
| 2. |
Let S be a set of n>0 elements. Let be the number Bᵣ of binary relations on S and let Bf be the number of functions from S to S. The expression for Bᵣ and Bf, in terms of n should be ____________ |
| A. | n² and 2(n+1)² |
| B. | n³ and n⁽ⁿ⁺¹⁾ |
| C. | n and n⁽ⁿ⁺⁶⁾ |
| D. | 2⁽ⁿ*ⁿ⁾ and nⁿ |
| Answer» E. | |
| 3. |
Let a set S = {2, 4, 8, 16, 32} and |
| A. | 6 |
| B. | 5 |
| C. | 9 |
| D. | 4 |
| Answer» C. 9 | |
| 4. |
Let A and B be two non-empty relations on a set S. Which of the following statements is false? |
| A. | A and B are transitive ⇒ A∩B is transitive |
| B. | A and B are symmetric ⇒ A∪B is symmetric |
| C. | A and B are transitive ⇒ A∪B is not transitive |
| D. | A and B are reflexive ⇒ A∩B is reflexive |
| Answer» D. A and B are reflexive ⇒ A∩B is reflexive | |
| 5. |
______ number of reflexive closure exists in a relation R = {(0,1), (1,1), (1,3), (2,1), (2,2), (3,0)} where {0, 1, 2, 3} ∈ A. |
| A. | 2⁶ |
| B. | 6 |
| C. | 8 |
| D. | 36 |
| Answer» C. 8 | |
| 6. |
The transitive closure of the relation {(0,1), (1,2), (2,2), (3,4), (5,3), (5,4)} on the set {1, 2, 3, 4, 5} is _______ |
| A. | {(0,1), (1,2), (2,2), (3,4)} |
| B. | {(0,0), (1,1), (2,2), (3,3), (4,4), (5,5)} |
| C. | {(0,1), (1,1), (2,2), (5,3), (5,4)} |
| D. | {(0,1), (0,2), (1,2), (2,2), (3,4), (5,3), (5,4)} |
| Answer» E. | |
| 7. |
R is a binary relation on a set S and R is reflexive if and only if _______ |
| A. | r(R) = R |
| B. | s(R) = R |
| C. | t(R) = R |
| D. | f(R) = R |
| Answer» B. s(R) = R | |
| 8. |
A partial order P is defined on the set of natural numbers as follows. Here a/b denotes integer division. i)(0, 0) ∊ P. ii)(a, b) ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs: |
| A. | (145, 265) and (0, 153) |
| B. | (22, 101) and (0, 153) |
| C. | (101, 22) and (145, 265) |
| D. | (101, 22) and (0, 153) |
| Answer» E. | |
| 9. |
Consider the binary relation, A = {(a,b) | b = a – 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is? |
| A. | {(a,b) | a >= b and a, b belong to {1, 2, 3}} |
| B. | {(a,b) | a > b and a, b belong to {1, 2, 3}} |
| C. | {(a,b) | a <= b and a, b belong to {1, 2, 3}} |
| D. | {(a,b) | a = b and a, b belong to {1, 2, 3}} |
| Answer» B. {(a,b) | a > b and a, b belong to {1, 2, 3}} | |
| 10. |
Let R₁ be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R₂ be another relation from B to C = {1, 2, 3, 4} as defined below: |
| A. | R₁R₂ = {(1, 2), (1, 4), (3, 3), (5, 4), (5,6), (7, 3)} |
| B. | Φ |
| C. | R₁R₂ = {(1, 2), (1,6), (3, 2), (3, 4), (5, 4), (7, 2)} |
| D. | R₁R₂ = {(2,2), (3, 2), (3, 4), (5, 1), (5, 3), (7, 1)} |
| Answer» C. R₁R₂ = {(1, 2), (1,6), (3, 2), (3, 4), (5, 4), (7, 2)} | |
| 11. |
For a, b ∈ Z define a | b to mean that a divides b is a relation which does not satisfy ___________ |
| A. | irreflexive and symmetric relation |
| B. | reflexive relation and symmetric relation |
| C. | transitive relation |
| D. | symmetric relation |
| Answer» C. transitive relation | |
| 12. |
Which of the following is an equivalence relation on R, for a, b ∈ Z? |
| A. | (a-b) ∈ Z |
| B. | (a²+c) ∈ Z |
| C. | (ab+cd)/2 ∈ Z |
| D. | (2c³)/3 ∈ Z |
| Answer» C. (ab+cd)/2 ∈ Z | |
| 13. |
Determine the number of possible relations in an antisymmetric set with 19 elements. |
| A. | 23585 |
| B. | 2.02 * 10⁸⁷ |
| C. | 9.34 * 7⁹¹ |
| D. | 35893 |
| Answer» C. 9.34 * 7⁹¹ | |
| 14. |
Determine the partitions of the set {3, 4, 5, 6, 7} from the following subsets. |
| A. | {3,5}, {3,6,7}, {4,5,6} |
| B. | {3}, {4,6}, {5}, {7} |
| C. | {3,4,6}, {7} |
| D. | {5,6}, {5,7} |
| Answer» C. {3,4,6}, {7} | |
| 15. |
Suppose X = {a, b, c, d} and π1 is the partition of X, π₁ = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by __________ |
| A. | 15 |
| B. | 10 |
| C. | 34 |
| D. | 5 |
| Answer» C. 34 | |
| 16. |
The binary relation U = Φ (empty set) on a set A = {11, 23, 35} is _____ |
| A. | Neither reflexive nor symmetric |
| B. | Symmetric and reflexive |
| C. | Transitive and reflexive |
| D. | Transitive and symmetric |
| Answer» E. | |
| 17. |
Consider the congruence 45≡3(mod 7). Find the set of equivalence class representatives. |
| A. | {…, 0, 7, 14, 28, …} |
| B. | {…, -3, 0, 6, 21, …} |
| C. | {…, 0, 4, 8, 16, …} |
| D. | {…, 3, 8, 15, 21, …} |
| Answer» B. {…, -3, 0, 6, 21, …} | |
| 18. |
The less-than relation, |
| A. | not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric |
| B. | a partial ordering since it is asymmetric and reflexive |
| C. | a partial ordering since it is antisymmetric and reflexive |
| D. | not a partial ordering because it is not antisymmetric and reflexive |
| Answer» B. a partial ordering since it is asymmetric and reflexive | |
| 19. |
Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________ |
| A. | equivalence relation |
| B. | reflexive relation |
| C. | symmetric relation |
| D. | transitive relation |
| Answer» B. reflexive relation | |
| 20. |
Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true? |
| A. | Every non-empty subset of has a greatest lower bound |
| B. | It is uncountable |
| C. | Every non-empty finite subset of has a least upper bound |
| D. | Every non-empty subset of has a least upper bound |
| Answer» B. It is uncountable | |
| 21. |
Determine the set of all integers a such that a ≡ 3 (mod 7) such that −21 ≤ x ≤ 21. |
| A. | {−21, −18, −11, −4, 3, 10, 16} |
| B. | {−21, −18, −11, −4, 3, 10, 17, 24} |
| C. | {−24, -19, -15, 5, 0, 6, 10} |
| D. | {−23, −17, −11, 0, 2, 8, 16} |
| Answer» C. {−24, -19, -15, 5, 0, 6, 10} | |
| 22. |
A partial order ≤ is defined on the set S = {x, b₁, b₂, … bₙ, y} as x ≤ bᵢ for all i and bᵢ ≤ y for all i, where n ≥ 1. The number of total orders on the set S which contain the partial order ≤ is ______ |
| A. | n+4 |
| B. | n² |
| C. | n! |
| D. | 3 |
| Answer» D. 3 | |
| 23. |
Amongst the properties {reflexivity, symmetry, antisymmetry, transitivity} the relation R={(a,b) ∈ N² | a!= b} satisfies _______ property. |
| A. | symmetry |
| B. | transitivity |
| C. | antisymmetry |
| D. | reflexivity |
| Answer» B. transitivity | |
| 24. |
Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, Nr) on A and the number of functions (say, Nf) from A to A? |
| A. | number of relations |
| B. | number of functions |
| C. | the element set |
| D. | number of subsets of the relation |
| Answer» B. number of functions | |
| 25. |
_________ number of reflexive relations are there on a set of 11 distinct elements. |
| A. | 2¹¹⁰ |
| B. | 3¹²¹ |
| C. | 2⁹⁰ |
| D. | 2¹³² |
| Answer» B. 3¹²¹ | |
| 26. |
________ is the rank of the largest equivalence relation on a set of 20 elements. |
| A. | 3²⁰ |
| B. | 2⁴⁰⁰ |
| C. | 20 |
| D. | 1 |
| Answer» E. | |
| 27. |
How many elements are there in the smallest equivalence relation on a set with 8 elements? |
| A. | 10² |
| B. | 8 |
| C. | 48 |
| D. | 32 |
| Answer» C. 48 | |
| 28. |
Suppose S is a finite set with 7 elements. How many elements are there in the largest equivalence relation on S? |
| A. | 56 |
| B. | 78 |
| C. | 49 |
| D. | 100 |
| Answer» D. 100 | |
| 29. |
The number of reflexive as well as symmetric relations on a set with 14 distinct elements is __________ |
| A. | 4¹²⁰ |
| B. | 2⁷⁰ |
| C. | 3²⁰¹ |
| D. | 2⁹¹ |
| Answer» E. | |
| 30. |
The number of symmetric relations on a set with 15 distinct elements is ______ |
| A. | 2¹⁹⁶ |
| B. | 2⁵⁰ |
| C. | 2³²⁰ |
| D. | 2⁷⁸ |
| Answer» B. 2⁵⁰ | |
| 31. |
How many binary relations are there on a set S with 9 distinct elements? |
| A. | 2⁹⁰ |
| B. | 2¹⁰⁰ |
| C. | 2⁸¹ |
| D. | 2⁶⁰ |
| Answer» D. 2⁶⁰ | |
| 32. |
Synonym for binary relation is _______ |
| A. | equivalence relation |
| B. | dyadic relation |
| C. | orthogonal relation |
| D. | one to many relations |
| Answer» C. orthogonal relation | |
| 33. |
The rank of smallest equivalence relation on a set with 12 distinct elements is _______ |
| A. | 12 |
| B. | 144 |
| C. | 136 |
| D. | 79 |
| Answer» B. 144 | |
| 34. |
If a set A has 8 elements and a set B has 10 elements, how many relations are there from A to B? |
| A. | 2⁹⁰ |
| B. | 3⁸⁰ |
| C. | 164 |
| D. | 2⁸⁰ |
| Answer» E. | |
| 35. |
Q: Pointing toward’s a boy, a girl said that he is the only son of my paternal aunt's daughter. How will my brother’s only daughter is related to that boy? |
| A. | Son |
| B. | Nephew |
| C. | Daughter |
| D. | Cousin |
| Answer» E. | |
| 36. |
How many females are there in the family? (Use the data if necessary from the previous question) |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | Cannot be determined |
| Answer» E. | |
| 37. |
Who is E’s father? (Use the data if necessary from the previous question) |
| A. | B |
| B. | A |
| C. | C |
| D. | G |
| Answer» C. C | |
| 38. |
If A is G’s son, how is A related to F? |
| A. | Uncle |
| B. | Father |
| C. | Cousin |
| D. | Brother |
| Answer» B. Father | |
| 39. |
If C is B’s husband, how is F related to E? |
| A. | Brother |
| B. | Sister |
| C. | Cousin |
| D. | Cannot be determined |
| Answer» D. Cannot be determined | |
| 40. |
How is D related to B? |
| A. | Sister |
| B. | Sister-in-law |
| C. | Mother |
| D. | Aunt |
| Answer» E. | |
| 41. |
Mr.Ramu’s mother’s father-in-law’s only son’s only daughter’s son is Chetan. How is Ramu related to Chetan? |
| A. | Uncle |
| B. | Nephew |
| C. | Niece |
| D. | Father |
| Answer» B. Nephew | |
| 42. |
A is the husband of B. E is the daughter of C. A is the father of C. How is B related to E? |
| A. | Mother |
| B. | Grandmother |
| C. | Aunt |
| D. | Cousin |
| Answer» C. Aunt | |
| 43. |
How is Radha’s mother’s mother’s daughter-in-law’s daughter related to Radha? |
| A. | Sister |
| B. | Mother |
| C. | Cousin |
| D. | Aunt |
| Answer» D. Aunt | |
| 44. |
Introducing a man to her husband, a woman said, “His brother’s father is the only son of my grandfather.” How is the woman related to this man? |
| A. | Mother |
| B. | Aunt |
| C. | Sister |
| D. | Daughter |
| Answer» D. Daughter | |
| 45. |
Pointing to Manju, Raju said, “The son of her only brother is the brother of my wife”. How is Manju related to Raju? |
| A. | Mother’s sister |
| B. | Grandmother |
| C. | Mother-in-law |
| D. | Sister of father-in-law |
| Answer» E. | |
| 46. |
A girl introduced a boy as the son of the daughter of the father of her uncle. How is the boy related to the girl? |
| A. | Brother |
| B. | Son |
| C. | Uncle |
| D. | Son-in-law |
| Answer» B. Son | |
| 47. |
If X is the brother of the son of Y’s son, how is X related to Y? |
| A. | Son |
| B. | Brother |
| C. | Cousin |
| D. | Grandson |
| Answer» E. | |
| 48. |
Pointing to a gentleman, Deepak said, “His only brother is the father of my daughter’s father”. How is the gentleman related to Deepak? |
| A. | Grandfather |
| B. | Father |
| C. | Brother-in-law |
| D. | Uncle |
| Answer» E. | |
| 49. |
Introducing a man to her husband, a woman said, “His brother’s father is the only son of my grandfather.”. How is the woman related to his man? |
| A. | Mother |
| B. | Aunt |
| C. | Sister |
| D. | Daughter |
| Answer» D. Daughter | |
| 50. |
Pointing to a lady, a girl said, “She is the daughter-in-law of the grandmother of my father’s only son.”How is the lady related to the girl? |
| A. | Sister-in-law |
| B. | Mother |
| C. | Aunt |
| D. | Mother-in-law |
| Answer» C. Aunt | |