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 2 of 9

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Q11.

__________ are called group postulates.

Group lemmas

Group theories

Group axioms

Group

Discuss

Answer: (c).Group axioms

Q12.

A subgroup has the properties of ________

Closure, associative

Commutative, associative, closure

Inverse, identity, associative

Closure, associative, Identity, Inverse

Discuss

Answer: (d).Closure, associative, Identity, Inverse

Q13.

If a * b = a such that a ∗ (b ∗ c) = a ∗ b = a and (a * b) * c = a * b = a then ________

* is associative

* is commutative

* is closure

* is abelian

Discuss

Answer: (a).* is associative

Q14.

The set of odd and even positive integers closed under multiplication is ________

a free semigroup of (M, ×)

a subsemigroup of (M, ×)

a semigroup of (M, ×)

a subgroup of (M, ×)

Discuss

Answer: (b).a subsemigroup of (M, ×)

Q15.

If F is a free semigroup on a set S, then the concatenation of two even words is ________

a semigroup of F

a subgroup of F

monoid of F

cyclic group of F

Discuss

Answer: (b).a subgroup of F

Q16.

The set of rational numbers form an abelian group under _________

Association

Closure

Multiplication

Addition

Discuss

Answer: (c).Multiplication

Q17.

Condition of semigroup homomorphism should be ____________

f(x * x) = f(x * y)

f(x) = f(y)

f(x) * f(y) = f(y)

f(x * y) = f(x) * f(y)

Discuss

Answer: (d).f(x * y) = f(x) * f(y)

Q18.

A function f:(M,∗)→(N,×) is a homomorphism if ______

f(a, b) = a*b

f(a, b) = a/b

f(a, b) = f(a)+f(b)

f(a, b) = f(a)*f(a)

Discuss

Answer: (b).f(a, b) = a/b

Q19.

A function defined by f(x)=2*x such that f(x+y)=2x+y under the group of real numbers, then ________

Isomorphism exists

Homomorphism exists

Heteromorphic exists

Association exists

Discuss

Answer: (b).Homomorphism exists

Q20.

If x * y = x + y + xy then (G, *) is _____________

Monoid

Abelian group

Commutative semigroup

Cyclic group

Discuss

Answer: (c).Commutative semigroup

Page 2 of 9

Welcome to the Group Theory MCQs Page

Group Theory MCQs | Page 2 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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