MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For a, b ∈ R define a = b to mean that |x| = |y|. If [x] is an equivalence relation in R. Find the equivalence relation for [17]. |
| A. | {,…,-11, -7, 0, 7, 11,…} |
| B. | {2, 4, 9, 11, 15,…} |
| C. | {-17, 17} |
| D. | {5, 25, 125,…} |
| Answer» D. {5, 25, 125,…} | |
| 2. |
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} | |
| 3. |
Which of the following is an equivalence relation on R, for a, b ∈ Z? |
| A. | (a-b) ∈ Z |
| B. | ∈ Zb) (a2+c) ∈ Z |
| C. | ∈ Zc) (ab+cd)/2 ∈ Z |
| D. | /2 ∈ Zd) (2c3)/3 ∈ Z |
| Answer» C. ∈ Zc) (ab+cd)/2 ∈ Z | |
| 4. |
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 | |
| 5. |
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 | |
| 6. |
Determine the number of equivalence classes that can be described by the set {2, 4, 5}. |
| A. | 125 |
| B. | 5 |
| C. | 16 |
| D. | 72 |
| Answer» C. 16 | |
| 7. |
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} | |
| 8. |
Which of the following relations is the reflexive relation over the set {1, 2, 3, 4}? |
| A. | {(0,0), (1,1), (2,2), (2,3)} |
| B. | {(1,1), (1,2), (2,2), (3,3), (4,3), (4,4)} |
| C. | {,(1,1), (1,2), (2,1), (2,3), (3,4)} |
| D. | {(0,1), (1,1), (2,3), (2,2), (3,4), (3,1) |
| Answer» C. {,(1,1), (1,2), (2,1), (2,3), (3,4)} | |
| 9. |
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, …} | |
| 10. |
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 | |