# 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:

1. An operation * on set A is a closed operation.
2. Operation * is an associative operation.
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

A semi-group is defined as one that satisfies these properties:

1. An operation * on set A is a closed operation.
2. 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 *.

1. Semigroups
2. Supersemigroups
3. Subsemigroups
4. None

Explanation:

Suppose we have a semigroup (A, *) and let B ⊆ A. Subsemigroups are formed when sets B are closed under operations *.

3. ' ° ' is a -

1. Grouping Operation
2. Concatenation Operation
3. Conversion Operation
4. None

Explanation:

' ° ' is a concatenation operation.

4. (A*,°) is a -

1. Semigroup
2. Subsemigroup
3. Supersemigroup
4. None

Explanation:

(A*,°) is a semigroup.

5. Semigroup (A*,°) generated by set A is known as -

1. Bound Semigroup
2. Free semigroup
3. Partial semigroup
4. Partially bound 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:

1. Set A can only be operated on by the operation o.
2. Associative operations are based on the o operation.
3. A unique element exists, namely the operation o.
4. 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:

1. Set A can only be operated on by the operation o.
2. Associative operations are based on the o operation.
3. 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) -

1. A closed operation is carried out under operation o.
2. It is possible to identify an element by its identity value e ∈ T.
3. Both A and B
4. 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) -

1. A closed operation is carried out under operation o.
2. It is possible to identify an element by its identity value e ∈ T.