Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Computer Engineering Expert

problem 1)a) Let (G, *) be a group. Let H be a non empty subset of G. Show that H is a subgroup if and only if a * b H, (ii) a-1 H, for all a, b H.

b) Demonstrate that every group of order less than or equal to five is abelian.

c) Demonstrate that in any group of even order there is non identity element a which is inverse of itself.

problem 2)a) State Kernel of homomorphism f from a group G,* to a group G ,0. Demonstrate that kernel of f is a normal subgroup of G.

b) Demonstrate that number of partitions of n is equal to number of partitions of 2n with exactly n parts.

c) By generating function technique find an expression for

(i) number of r combinations of n objects with unlimited repetition.

(ii) number of combinations of n with exactly m parts.

problem 3)a) Prove that the number of partitions of n in which no integer occurs more than twice as a part is equal to the number of partitions of n into parts not divisible by 3.

b) Demonstrate that a graph G is a tree if and only if between every two vertices there exists unique path.

problem 4)a) Demonstrate that a connected graph is Eulerian if and only if all of its vertices are of even degree.

b) If the meet operation is distributive over the join operation in a lattice, then show that the join operation is also distributive over the meet operation.

c) State principle of inclusion and exclusion. Determine the number of permutations of n objects 1, 2, …..,n in which no object occupies its proper place. What happens as n tends to infinity?

problem 5)a) Let E x1,x2,x3 x1 x2 x1 x3 x2 x3 be a Boolean algebra . prepare E x1,x2,x3 in both disjunctive and conjunctive normal forms.

b) Prove that

(?x) (P(x) Λ Q(x)) => ( ? x) (P(x) Λ ( ? x) Q(x) . Given suitable ex to show that this converse is no true.

Computer Engineering, Engineering

  • Category:- Computer Engineering
  • Reference No.:- M96568

Have any Question? 


Related Questions in Computer Engineering

Sketch out a class diagram uml for the candidate classes

Sketch out a class diagram (UML) for the candidate classes you list from the description provided. You should have AT LEAST ONE generalization relationship and AT LEAST ONE composition relationship: The library system ne ...

Briefly explain the history and evolution of system safety

Briefly explain the history and evolution of system safety as well as the components and theory of an SMS. Discuss the roles of the ICAO, the FAA and other State safety programs in aviation safety management. Analyze the ...

Describe the function point analysis technique for deriving

Describe the Function Point Analysis technique for deriving effort and cost estimates for software projects? Describe the COCOMO technique for deriving effort and cost estimates for software projects?

App inventor1create an app inventor app that calculates and

App Inventor 1. Create an App Inventor app that calculates and displays a circle's area and circumference. Ask users to supply a radius for the circle. 2. Create an App Inventor app that calculates and displays a rectang ...

Explain in general terms how the traditional e-r model the

Explain, in general terms, how the traditional E-R model, the IE Crow's Foot version, the IDEF1X version, and the UML version differ. Which version is used primarily in this text?

Explain the use of the sql begin transaction commit

Explain the use of the SQL BEGIN TRANSACTION, COMMIT TRANSACTION, and ROLLBACK TRANSACTION statements. Why does MySQL also use the SQL START TRANSACTION statement?

Assume process p1 has threads t1 and t2 will t1 and t2

Assume process P1 has threads T1 and T2. Will T1 and T2 continue to run after P1 exits? Explain your answer.

A consumer has a utility function nbspu x1nbspx2 x12nbsp

A consumer has a utility function :  u (x 1,  x 2 ) = (x 1 ) 2  + (x 2 ) 2  . The consumer has an income m = 10 and can buy goods at the prices (p 1 , p 2 ) = (2, 1). What is the consumer's utility maximizing choice?

A find a simple nondeterministic finite-state machine

a) Find a simple nondeterministic finite-state machine accepting the language (01 ∪ 001 ∪ 010)∗ over Σ = {0, 1}. b) Convert the nondeterministic finite state machine of part (a) to a deterministic finite-state machine by ...

Do you see any problems with the choice of hash functions

Do you see any problems with the choice of hash functions in Exercise 4.4.1? What advice could you give someone who was going to use a hash function of the form h(x) = ax + b mod 2 k ? Exercise 4.4.1 Suppose our stream c ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate