MCQOPTIONS
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MCQOPTIONS
This section includes 8 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. |
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 | |
| 2. |
Consider the ordering relation a | b ⊆ N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________a) | is an equivalence relationb) It is a total orderc) Every subset of N has an upper bound under |d) (N, |
| A. | | is an equivalence relation |
| B. | It is a total order |
| C. | Every subset of N has an upper bound under | |
| D. | (N,|) is a lattice but not a complete lattice |
| Answer» E. | |
| 3. |
The inclusion of ______ sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment. |
| A. | {1}, {2, 4} |
| B. | {1}, {1, 2, 3} |
| C. | {1} |
| D. | {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5} |
| Answer» D. {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5} | |
| 4. |
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:i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)The ordered pairs of natural numbers are contained in P are ______ and ______ |
| A. | (145, 265) and (0, 153) |
| B. | ∊ P if and only if a % 10 ≤ b % 10 and (a/10, b/10) ∊ P. Consider the following ordered pairs:i. (101, 22) ii. (22, 101) iii. (145, 265) iv. (0, 153)The ordered pairs of natural numbers are contained in P are ______ and ______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. | |
| 5. |
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 | |
| 6. |
If the longest chain in a partial order is of length l, then the partial order can be written as _____ disjoint antichains. |
| A. | l2 |
| B. | l+1 |
| C. | l |
| D. | ll |
| Answer» D. ll | |
| 7. |
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 | |
| 8. |
Let a set S = {2, 4, 8, 16, 32} and |
| A. | 6 |
| B. | 5 |
| C. | 9 |
| D. | 4 |
| Answer» C. 9 | |