Ask Question, Ask an Expert


Ask Computer Engineering Expert


a)  Make truth table for 

i) p→(~q ? ~ r) ? ~p ?  q

ii) ~p→~r ? q ? ~p ? r

b) If A = {1, 2, 3, 4, 5,6,7,8, 9} B = {2, 3, 5, 6, 7} Then find A Δ B .

c) prepare down appropriate mathematical statement which could be represented by following symbolic properties.

i) (∀ x) (∀y) (∃ z) P

ii) ∀(x) (∃y) (∃z) P

problem 2)

a) Define  proof? Describe how direct proof is different from indirect proof. Describe method of direct proof with the help of an ex.

b) Show if √11 is rational or irrational.

c) Consider a set X = [2, 3, 4) and the Relation defined on X by.

R = {(2, 2) (2, 3) (3, 3) (3, 4) (2, 4) (4, 4)}. Find whether R is :

i) Reflexive

ii) Symmetric

iii) Transitive

Also justify your answer.

problem 3:

a) Survey among students of college. 60 Study Hindi, 40 study Spanish, and 45 study Japanese, Further 20 study Hindi and Spanish, 25 study Hindi and Japanese, 15 study Spanish and Japanese and 8 study all the languages. Determine the followings:

i) How many students are studying at least one language?

ii) How many students are studying only Hindi?

iii) How many students are studying only Japanese?

b) If p and q are statements, show if the statement [(~p→q) ? (~q)] → (~p ? ~q)  is a tautology or not.

problem 4:

a) Make logic circuit for the following Boolean expressions:

i)  (x′ ? y ? z) + (x ? y ? z)′

ii) ( x' ? y) ? (y′ ? z) ? (y ? z′)

iii) (x ? y)  ? (y ?  z)

b) Describe principle of duality. Determine dual of Boolean expression of the output of the following logic circuit:

1440_Logic circuit.jpg

c) Set A,B and C are:

A = {1, 2, 4, 5,6,19},  B = { 1,2,5,22, 44 } and C { 2, 5,11,19,25,40}, Find A ∩ B ∪ C and A ∪ B ∪ C.

problem 5:

a) Draw the Venn diagram to represent following:

i)  (A  Δ B) ∩  (C~B)

ii)    (A ∪ B) ∩  (B Δ C)

b) describe relation mathematically. Also give at least two ex of relations.

c) Show that n3 + 2n is divisible by 3 for all  n≥ 1 by induction.

problem 6:

a) Describe inclusion-exclusion principle? Also describe one application of inclusion-exclusion principle.

b)   If f : R → R is a function such that  f (x) = 3x + 5, prove that f  is one - one onto. Also determine the inverse of f.

problem 7:

a) Find how many 3 digit numbers are even? How many 3 digit numbers are composed of odd digits?

b) How many different 15 persons committees could be formed each containing at least 4 Project Managers and at least 3 Programmers from the set of 10 Project Managers and 10 Programmers?

c) Assume we have ten rooms and want to allot five of them to five programmers as offices and use remaining five rooms for computer terminals. Describe in how many ways this could be done.

problem 8:

a) describe Demorgan’s Law? Describe use of Demorgan’s law with an ex.

b)  Two dice, one red and one white are rolled. What is the probability that the white die turns up a smaller number than the red die ?

c) Describe pigeon hole principle. Using this principle demonstrate that in any group of 36 people, we could always find 6 people who were born on the same day of week.


Computer Engineering, Engineering

  • Category:- Computer Engineering
  • Reference No.:- M92152

Have any Question? 

Related Questions in Computer Engineering

Part 1 determine your ip addresslook up the difference

Part 1: Determine your I/P address Look up the difference between public and private IP addresses.  Create a word processor document and explain, in your own words, the difference between the two.  Then determine your pu ...

Abstract data types adts are very important as they serve

Abstract data types (ADTs) are very important as they serve as programming tools that enable component reuse and encapsulation. This assignment requires students to create, implement and apply ADTs in an application.The ...

1 in extension 1 of the fire simple model there are two

1. In extension 1 of the Fire Simple model, there are two parameters governed by sliders, DENSITY and PROBABILITY-OF-SPREAD. How do these two interact with regard to a critical spread of the fire? 2. The original Fire Si ...

1 compare the medium of a wired lan with that of a wireless

1. Compare the medium of a wired LAN with that of a wireless LAN in today's communication environment. 2. Explain why the MAC protocol is more important in wireless LANs than in wired LANs. 3. Explain why there is more a ...

Write a c program that fills random squares of 3 by 3 with

Write a C++ program that fills random squares of 3 by 3, with unique numbers from 1 to 9, and tests if the generated matrix forms a Magic Squares. Your program should loop until  three magic squares  are generated and  p ...

How might xyz software company arrive at the values in the

How might XYZ Software Company arrive at the values in the above table? For each entry, describe the process of determining the cost per incident and frequency of occurrence.

Discuss authorization and authentication and explain

Discuss authorization and authentication and explain forms-based-authentication. Describe the use of the ControlToValidate, Validation expression, ErrorMessage, and Enabled properties of a validation control.

Suppose a directed network takes the form of a tree with

Suppose a directed network takes the form of a tree with all edges pointing inward towards a central vertex: What is the PageRank centrality of the central vertex in terms of the single parameter a appearing in the defin ...

1nbsptcos 3 and 5 in windows 7 how do you open the task

1.  (TCOs 3 and 5) In Windows 7, how do you open the Task Manager? On the Processes tab, name, and describe at least three parameters that are displayed by default. Should be at least one paragraph

1 using rfc 1939 assume a pop3 client is in the

1. Using RFC 1939, assume a POP3 client is in the download-and-keep mode. Show the transaction between the client and the server if the client has only two messages of 192 and 300 bytes to download from the server. 2. Us ...

  • 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

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

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen