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Discrete Mathematics | Partially Ordered Sets MCQs
Discrete Mathematics | Partially Ordered Sets MCQs: This section contains multiple-choice questions and answers on Partially Ordered Sets in Discrete Mathematics.
Submitted by Anushree Goswami, on November 01, 2022
1. Which of the following properties are satisfied by the relation R on the set S?
- A reflexive function (R) returns xRx when x ∈ S.
- There is an antisymmetry in R, so if xRy and yRx, then x = y.
- The R function is transitive; if xRy and yRz, then xRz follows.
- All of the above
Answer: D) All of the above
Explanation:
The following properties are satisfied by the relation R on the set S:
- A reflexive function (R) returns xRx when x ∈ S.
- There is an antisymmetry in R, so if xRy and yRx, then x = y.
- The R function is transitive; if xRy and yRz, then xRz follows.
2. ____ relationships are referred to as R.
- Ordered
- Unordered
- Partially ordered
- Partially unordered
Answer: C) Partially ordered
Explanation:
Partially ordered relationships are referred to as R.
3. A partially ordered set (_____) is a set with partial order combined with S.
- POSET
- PASET
- PAOET
- POS
Answer: A) POSET
Explanation:
A partially ordered set (POSET) is a set with partial order combined with S.
4. POSET is denoted by -
- (≤, S)
- (S, ≤)
- (>=, S)
- (S, >=)
Answer: B) (S, ≤)
Explanation:
POSET is denoted by (S, ≤).
5. ____ elements of A are those where a ≤ c in A does not contain elements in c.
- Maximal
- Minimal
- Both A and B
- None of the above
Answer: A) Maximal
Explanation:
Maximal elements of A are those where a ≤ c in A does not contain elements in c.
6. A _____ element of A is a data structure in which the element in c in A cannot be changed.
- Maximal
- Minimal
- Both A and B
- None of the above
Answer: B) Minimal
Explanation:
A minimal element of A is a data structure in which the element in c in A cannot be changed.
7. It is possible to have ___ maximal element or ___ minimal element.
- One, more than one
- Two, more than one
- More than one, more than one
- More than one, Zero
Answer: C) More than one, more than one
Explanation:
It is possible to have more than one maximal element or more than one minimal element.
8. A pair of elements a and b of set A is comparable if -
- a ≤ b
- b ≤ a
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
A pair of elements a and b of set A is comparable if a ≤ b or b ≤ a.
9. In set A, two elements a and b cannot be compared even if neither ____.
- a ≤ b
- b ≤ a
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
In set A, two elements a and b cannot be compared even if neither a ≤ b nor b ≤ a.
10. When all elements in set A are comparable, it's called a ____.
- Linearly Ordered Set
- Totally Ordered Set
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
When all elements in set A are comparable, it's called a linearly ordered set or a totally ordered set.