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Discrete Mathematics | SemiGroup MCQs
Discrete Mathematics | SemiGroup MCQs: This section contains multiple-choice questions and answers on SemiGroup in Discrete Mathematics.
Submitted by Anushree Goswami, on October 29, 2022
1. A semi-group is defined as one that satisfies these properties:
- An operation * on set A is a closed operation.
- Operation * is an associative operation.
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
A semi-group is defined as one that satisfies these properties:
- An operation * on set A is a closed operation.
- Operation * is an associative operation.
2. Suppose we have a semigroup (A, *) and let B ⊆ A. ____ are formed when sets B are closed under operations *.
- Semigroups
- Supersemigroups
- Subsemigroups
- None
Answer: C) Subsemigroups
Explanation:
Suppose we have a semigroup (A, *) and let B ⊆ A. Subsemigroups are formed when sets B are closed under operations *.
3. ' ° ' is a -
- Grouping Operation
- Concatenation Operation
- Conversion Operation
- None
Answer: B) Concatenation Operation
Explanation:
' ° ' is a concatenation operation.
4. (A*,°) is a -
- Semigroup
- Subsemigroup
- Supersemigroup
- None
Answer: A) Semigroup
Explanation:
(A*,°) is a semigroup.
5. Semigroup (A*,°) generated by set A is known as -
- Bound Semigroup
- Free semigroup
- Partial semigroup
- Partially bound semigroup
Answer: B) Free semigroup
Explanation:
Semigroup (A*,°) generated by set A is known as Free semigroup.
6. The algebraic system (A, o) consists of the binary operation o on A. If (A, o) satisfies the following property/ies, then it is said to be a monoid:
- Set A can only be operated on by the operation o.
- Associative operations are based on the o operation.
- A unique element exists, namely the operation o.
- All of the above
Answer: D) All of the above
Explanation:
The algebraic system (A, o) consists of the binary operation o on A. If (A, o) satisfies the following properties, then it is said to be a monoid:
- Set A can only be operated on by the operation o.
- Associative operations are based on the o operation.
- A unique element exists, namely the operation o.
7. When (S, o) satisfies the following properties, then it is called a submonoid of (M, o) -
- A closed operation is carried out under operation o.
- It is possible to identify an element by its identity value e ∈ T.
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
When (S, o) satisfies the following properties, then it is called a submonoid of (M, o) -
- A closed operation is carried out under operation o.
- It is possible to identify an element by its identity value e ∈ T.