# 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?

1. A reflexive function (R) returns xRx when x ∈ S.
2. There is an antisymmetry in R, so if xRy and yRx, then x = y.
3. The R function is transitive; if xRy and yRz, then xRz follows.
4. All of the above

Answer: D) All of the above

Explanation:

The following properties are satisfied by the relation R on the set S:

1. A reflexive function (R) returns xRx when x ∈ S.
2. There is an antisymmetry in R, so if xRy and yRx, then x = y.
3. The R function is transitive; if xRy and yRz, then xRz follows.

2. ____ relationships are referred to as R.

1. Ordered
2. Unordered
3. Partially ordered
4. Partially unordered

Explanation:

Partially ordered relationships are referred to as R.

3. A partially ordered set (_____) is a set with partial order combined with S.

1. POSET
2. PASET
3. PAOET
4. POS

Explanation:

A partially ordered set (POSET) is a set with partial order combined with S.

4. POSET is denoted by -

1. (≤, S)
2. (S, ≤)
3. (>=, S)
4. (S, >=)

Explanation:

POSET is denoted by (S, ≤).

5. ____ elements of A are those where a ≤ c in A does not contain elements in c.

1. Maximal
2. Minimal
3. Both A and B
4. None of the above

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.

1. Maximal
2. Minimal
3. Both A and B
4. None of the above

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.

1. One, more than one
2. Two, more than one
3. More than one, more than one
4. 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 -

1. a ≤ b
2. b ≤ a
3. Both A and B
4. 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 ____.

1. a ≤ b
2. b ≤ a
3. Both A and B
4. 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 ____.

1. Linearly Ordered Set
2. Totally Ordered Set
3. Both A and B
4. 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.

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