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Discrete Mathematics Multiple Choice Questions | MCQs | Quiz

Discrete Mathematics Interview Questions and Answers
Practice Discrete Mathematics questions and answers for interviews, campus placements, online tests, aptitude tests, quizzes and competitive exams.

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•   Propositions
•   Logic & Bit Operations
•   Implications
•   Logic Circuits
•   De-Morgan's Laws
•   Tautologie & Contradictions
•   Statements Types
•   Logical Equivalences
•   Predicate Logic Quantifiers
•   Nested Quantifiers
•   Inference
•   Proofs Types
•   Set Types
•   Sets
•   Set Operations - 1
•   Set Operations - 2
•   Venn Diagram
•   Algebraic Laws on Sets
•   Cartesian Product of Sets
•   Subsets
•   Functions
•   Functions Growth
•   Functions Range
•   Number of Functions
•   Floor & Ceiling Function
•   Inverse of a Function
•   Arithmetic Sequences
•   Geometric Sequences
•   Arithmetic Mean
•   Special Sequences
•   Harmonic Sequences
•   Cardinality of Sets
•   Matrices Types
•   Matrices Operations
•   Matrices Properties
•   Transpose of Matrices
•   Inverse of Matrices
•   Sequences & Summations
•   Algorithms
•   Algorithms Types
•   Algorithms Complexity - 1
•   Algorithms Complexity - 2
•   Integers & Algorithms
•   Integers & Division
•   Prime Numbers
•   Quadratic Residue
•   Least Common Multiples
•   Highest Common Factors
•   Base Conversion
•   Complement of a Number
•   Exponents Rules
•   Number Theory Applications
•   Greatest Common Divisors
•   Modular Exponentiation
•   Cryptography Encryption
•   Cryptography Decryption
•   Ciphers
•   Mathematical Induction
•   Strong Induction
•   Recursion
•   Counting Principle
•   Pigeonhole Principle
•   Linear Permutation
•   Circular Permutations
•   Combinations
•   Divisors - Number & Sum
•   Objects Division
•   Equations Solution
•   Derangements
•   Binomial Expansion Terms
•   Binomial Coefficient
•   Recurrence Relation
•   ↓ Probability ↓
•   Addition Theorem
•   Multiplication Theorem
•   Geometric Probability
•   Probability Distribution
•   Random Variables
•   Bayes Theorem
•   Generating Functions
•   Exclusion Principle
•   Logarithmic Series
•   Power Series
•   Number of Relations
•   Relations Closure
•   Relations Types
•   Partial Orderings
•   Equivalence Classes
•   Diagraph
•   Hasse Diagrams
•   Lattices
•   Bipartite Graphs
•   Graphs Properties
•   Connected Graphs
•   Graphs Isomorphism
•   Graph - Different Path
•   Degree & Graph Coloring
•   Graph's Matrices
•   Tree Properties
•   Cycles
•   Tree Traversal
•   Notations Interconversion
•   Spanning Trees
•   Boolean Algebra
•   Boolean Functions
•   Functions Minimization
•   Karnaugh Maps
•   Gates Interconversion
•   Prime Implicants
•   Finite State Automation
•   Group Theory
•   Group Axioms
•   Closure & Associativity
•   Identity & Inverse Existence
•   Subgroups
•   Cosets
•   Cyclic Groups
•   Permutation Groups
•   Burnside Theorem

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Discrete Mathematics Questions and Answers – Cosets

Posted on August 17, 2017 by Manish

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Cosets”.

1. a * H is a set of _____ coset.
a) right
b) left
c) sub
d) semi
View Answer

Answer: b
Explanation: Let (H, *) be the semigroup of the group (G, *). Let a belongs to G. (a * H) is the set of a left coset of H in G and (H * a) be the set of a right coset of H in G.
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2. a * H = H * a relation holds if __________
a) H is semigroup of an abelian group
b) H is monoid of a group
c) H is a cyclic group
d) H is subgroup of an abelian group
View Answer

Answer: d
Explanation: If h is the subgroup of an abelian group G, then the set of left cosets of H in G is to be set of right cosets i.e, a * H = H * a. Hence, subgroup is called the normal subgroup.

3. Lagrange’s theorem specifies __________
a) the order of semigroup is finite
b) the order of the subgroup divides the order of the finite group
c) the order of an abelian group is infinite
d) the order of the semigroup is added to the order of the group
View Answer

Answer: b
Explanation: Lagrange’s theorem satisfies that the order of the subgroup divides the order of the finite group.

4. A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called ______
a) isomorphic
b) homomorphic
c) cyclic group
d) heteromorphic
View Answer

Answer: a
Explanation: Let (G,*) and (G’,+) are two groups. The mapping f:G->G’ is said to be isomorphism if two conditions are satisfied 1) f is one-to-one function and onto function and 2) f satisfies homomorphism.

5. An isomorphism of a group onto itself is called ____
a) homomorphism
b) heteromorphism
c) epimorphism
d) automorphism
View Answer

Answer: d
Explanation: An automorphism is defined as an isomorphism of a group onto itself. Similarly, the homomorphism of a group onto itself is defined as the endomorphism of the group.
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6. The elements of a vector space form a/an ____ under vector addition.
a) abelian group
b) commutative group
c) associative group
d) semigroup
View Answer

Answer: a
Explanation: An example of a coset is associated with the theory of vector spaces. The elements (vectors) form an abelian group under the vector addition in a vector space. Subspaces of a vector space are subgroups of this group.

7. A set of representatives of all the cosets is called _________
a) transitive
b) reversal
c) equivalent
d) transversal
View Answer

Answer: d
Explanation: A coset representative is a representative in the equivalence class. In all cosets, a set of the representative is always transversal.

8. Which of the following statement is true?
a) The set of all rational negative numbers forms a group under multiplication
b) The set of all matrices forms a group under multiplication
c) The set of all non-singular matrices forms a group under multiplication
d) The set of matrices forms a subgroup under multiplication
View Answer

Answer: c
Explanation: Since multiplication of two negative rational numbers gives a positive number. Hence, closure property is not satisfied. Singular matrices do not form a group under multiplication. Matrices have to be non-singular (determinant !=0) for the inverse to exist. Hence the set of all non-singular matrices forms a group under multiplication is true option.

9. How many different non-isomorphic Abelian groups of order 8 are there?
a) 5
b) 4
c) 2
d) 3
View Answer

Answer: c
Explanation: The number of Abelian groups of order Pm (let, P is prime) is the number of partitions of m. Here order is 8 i.e. 23 and so partition of 3 are {1, 1} and {3, 0}. So number of different abelian groups are 2.

10. Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings ________
a) does not form a group
b) does not have the right identity element
c) forms a non-commutative group
d) forms a group if the empty string is removed from
View Answer

Answer: a
Explanation: Identity element for concatenation is an empty string. Now, we cannot concatenate any string with a given string to get empty string there is no inverse for string concatenation. Only other 3 group properties such as closure, associative and existence of identity are satisfied.
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Sanfoundry Global Education & Learning Series – Discrete Mathematics.

To practice all areas of Discrete Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Discrete Mathematics Questions and Answers – Cyclic Groups »
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Manish Bhojasia
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Facebook | Twitter

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