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

1 consider proposed implementations of a systolic array you

1. Consider proposed implementations of a systolic array (you can find these in on the Internet or in technical publications). Then attempt to program the loop provided in Exercise 6.11 using this MISD model. Discuss any ...

The fibonacci sequence starts 1 1 2 3 5 8 each number in

The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, . . .. Each number in the sequence (after the first two) is the sum of the previous two. Write a program that computes and outputs the nth Fibonacci number, where n is a va ...

1 what is an event object an event source an event

1. What is an event object? An event source? An event listener? 2. From a programmer's perspective, what is the most important difference between the user interfaces of a console application and a graphical application?

1 what is a hash function and what can it be used for2 why

1. What is a hash function, and what can it be used for? 2. Why is it important to exchange keys out of band in symmetric encryption? 3. What is the fundamental difference between symmetric and asymmetric encryption?

Given an example of broadcast usage in the network and data

Given an example of broadcast usage in the network and data link layers. For each case, (1) name the protocol that utilizing the broadcast, (2) the reason why the broadcast rather that unicast is used, and (3) how the fa ...

Question 1 an example of the neuron model is the sigmoid

Question 1. An example of the neuron model is the sigmoid function which is defined by: φ(v)=1/(1+exp?(-v)) For this problem, you need to prove that (∂φ(v))/∂v=φ(v)(1-φ(v)) Question 2. Consider the following cost functio ...

1 what does cissp stand for use the internet to identify

1. What does CISSP stand for? Use the Internet to identify the ethical rules CISSP holders have agreed to follow. 2. For what kind of information security jobs does the NSA recruit? Use the Internet to visit its Web page ...

1 name two accessor methods and two mutator methods of the

1. Name two accessor methods and two mutator methods of the Rectangle class. 2. Look into the API documentation of the Rectangle class and locate the method Read through the method documentation. Then determine the resul ...

The little languages presented in section 29323 have

The little languages presented in Section 29.3.2.3 have ambiguous semantics. For example, in the location language, does "not host1 or host2" mean "not at host1 and not at host2" or "not at host1, or at host2"? a. Rewrit ...

The following questions are related to the sparse matrix

The following questions are related to the Sparse Matrix ADT. (a) Implement the remaining methods of the SparseMatrix class presented in the chapter using the array of sorted linked lists: getitem , transpose(), sub , an ...

  • 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

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro