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

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 -

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

Answer: B) Concatenation Operation

Explanation:

' ° ' is a concatenation operation.


4. (A*,°) is a -

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

Answer: A) Semigroup

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

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:

  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.





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