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# Discrete Mathematics | Multisets MCQs

**Discrete Mathematics | Multisets MCQs**: This section contains multiple-choice questions and answers on Multisets in Discrete Mathematics.

Submitted by Anushree Goswami, on July 10, 2022

**1. In a multiset, elements are arranged in an unordered manner, with elements having a multiplicity of _____?**

- One
- More than one
- Zero
- All of the above

**Answer:** D) All of the above

**Explanation:**

In a multiset, elements are arranged in an unordered manner, with elements having a multiplicity of one, more than one, or none.

**2. In a multiset, multiplicity refers to the ____ with which an element is repeated.**

- Frequency
- Audacity
- Range
- Sequence

**Answer:** A) Frequency

**Explanation:**

In a multiset, multiplicity refers to the frequency with which an element is repeated.

**3. Which of the following is/are an/the operation(s) on multisets?**

- Union of Multisets
- Intersection of Multisets
- Difference of Multisets
- All of the above

**Answer:** D) All of the above

**Explanation:**

The following are the operations on multisets -

- Union of Multisets
- Intersection of Multisets
- Difference of Multisets

**4. As the multisets A and B are unions, their multiplicities are equal and denoted by A ∪ B. A ∪ B represents a multiset where the multiplicity of an element ____ the maximum of its multiplicities in both sets?**

- Is greater than
- Is lesser than
- Equals
- Equivalent to

**Answer:** C) Equals

**Explanation:**

As the multisets A and B are unions, their multiplicities are equal and denoted by A ∪ B. A ∪ B represents a multiset where the multiplicity of an element equals the maximum of its multiplicities in both sets.

**5. A multiset intersecting with another multiset, B, has a multiplicity equal to the minimum of the multiplicity of an element in each set, and is denoted by ___?**

- A ∩ B
- A ∪ B
- A * B
- A + B

**Answer:** A) A ∩ B

**Explanation:**

A multiset intersecting with another multiset, B, has a multiplicity equal to the minimum of the multiplicity of an element in each set, and is denoted by A ∩ B.

**6. Multisets are considered difference multisets if there is a _____ difference between them. An element's multiplicity of an element is equal to the multiplicity of the element in A minus the multiplicity of the element in B?**

- Positive
- Negative
- Both A and B
- None of the above

**Answer:** C) Both A and B

Multisets are considered difference multisets if there is a positive or negative difference between them. An element's multiplicity of an element is equal to the multiplicity of the element in A minus the multiplicity of the element in B.

**7. A multiset whose multiplicity equals the ___ of an element in two multisets A and B is called a multiset whose multiplicity equals the multiplicity of that element in two multisets?**

- Sum
- Minus
- Multiply
- Division

**Answer:** A) Sum

**Explanation:**

A multiset whose multiplicity equals the sum of an element in two multisets A and B is called a multiset whose multiplicity equals the multiplicity of that element in two multisets.

**8. When a multiset is called cardinal, it refers to the number of ____ elements without taking into account their multiplicity?**

- Distinct
- Similar
- Average
- Real

**Answer:** A) Distinct

**Explanation:**

When a multiset is called cardinal, it refers to the number of distinct elements without taking into account their multiplicity.

**9. A set of distinct objects that is ordered is referred to as an ____ set?**

- Unordered
- Ordered
- Distinct
- Indistinct

**Answer:** B) Ordered

**Explanation:**

A set of distinct objects that is ordered is referred to as an ordered set.

**10. ___ elements form an Ordered Pair, with the first element being designated as the first member and the second element being designated as the second member?**

- Two
- Three
- Four
- Multiple

**Answer:** A) Two

**Explanation:**

Two elements form an Ordered Pair, with the first element being designated as the first member and the second element being designated as the second member.

**11. If there are two ordered pairs, then an ordered triple would be written as ____?**

- {(a, b, c)}
- {(a, b)) c)}
- (a, b) c}
- {(a, b) c}

**Answer:** D) {(a, b) c}

**Explanation:**

If there are two ordered pairs, then an ordered triple would be written as {(a, b) c}.

**12. In an ordered quadrable, the first element is an ordered triple and it is denoted by ____?**

- {(((a, b, c)) d)}
- {((a, b), c) d)}
- {(a, b), c) d)}
- {(((a, b), c) d)}

**Answer:** D) {(((a, b), c) d)}

**Explanation:**

In an ordered quadrable, the first element is an ordered triple and it is denoted by {(((a, b), c) d)}.

**13. The first element of an ordered n-tuple is an ordered (____) tuple, while the nth element is an ordered n-tuple?**

- n
- n+1
- n-1
- n^2

**Answer:** C) n-1

**Explanation:**

The first element of an ordered n-tuple is an ordered (n - 1) tuple, while the nth element is an ordered n-tuple.

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