Welcome to the Group Theory MCQs Page

Dive deep into the fascinating world of Group Theory with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Group Theory, a crucial aspect of Discrete Mathematics. In this section, you will encounter a diverse range of MCQs that cover various aspects of Group Theory, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Discrete Mathematics.

Check out the MCQs below to embark on an enriching journey through Group Theory. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Discrete Mathematics.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Group Theory. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Group Theory MCQs | Page 1 of 9

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Logics and Proofs

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Q1.

A non empty set A is termed as an algebraic structure ________

with respect to binary operation *

with respect to ternary operation ?

with respect to binary operation +

with respect to unary operation –

Discuss

Answer: (a).with respect to binary operation *

Q2.

An algebraic structure _________ is called a semigroup.

(P, *)

(Q, +, *)

(P, +)

(+, *)

Discuss

Answer: (a).(P, *)

Q3.

Condition for monoid is __________

(a+e)=a

(a*e)=(a+e)

a=(a*(a+e)

(a*e)=(e*a)=a

Discuss

Answer: (d).(a*e)=(e*a)=a

Q4.

A monoid is called a group if _______

(a*a)=a=(a+c)

(a*c)=(a+c)

(a+c)=a

(a*c)=(c*a)=e

Discuss

Answer: (d).(a*c)=(c*a)=e

Q5.

A group (M,*) is said to be abelian if ___________

(x+y)=(y+x)

(x*y)=(y*x)

(x+y)=x

(y*x)=(x+y)

Discuss

Answer: (b).(x*y)=(y*x)

Q6.

Matrix multiplication is a/an _________ property.

Commutative

Associative

Additive

Disjunctive

Discuss

Answer: (b).Associative

Q7.

A cyclic group can be generated by a/an ________ element.

singular

non-singular

inverse

multiplicative

Discuss

Answer: (a).singular

Q8.

How many properties can be held by a group?

Discuss

Answer: (c).5

Q9.

A cyclic group is always _________

abelian group

monoid

semigroup

subgroup

Discuss

Answer: (a).abelian group

Q10.

{1, i, -i, -1} is __________

semigroup

subgroup

cyclic group

abelian group

Discuss

Answer: (c).cyclic group

Page 1 of 9

Welcome to the Group Theory MCQs Page

Group Theory MCQs | Page 1 of 9

Explore more Topics under Discrete Mathematics

Logics and Proofs

Sets and Functions

Sequences,Sums and Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting Theory

Discrete Probability

Relations

Graphs and Graphs Properties

Tree Properties

Boolean Algebra and Modeling Computations

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