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

1 what are the reuse time thresholds for these three

1. What are the reuse time thresholds for these three technology generations? 2. What are the reuse time thresholds if we keep using the same 4K page size? What's the trend here? 3. What other factors can be changed to k ...

1 in tcp how do we define the sequence number of a segment

1. In TCP, how do we define the sequence number of a segment (in each direction)? Consider two cases: the first segment and other segments. 2. In TCP, we have two consecutive segments. Assume the sequence number of the f ...

Implement the fibonacci algorithm as a function that

Implement the Fibonacci algorithm as a function that accepts as input two consecutive Fibonacci numbers and returns as output the next Fibonacci number.

How can us companies protect their digital assets

How Can U.S. Companies Protect their Digital Assets Overseas? Prepare a 3 to 5 paragraph briefing statement that can be used to answer the above question. Your audience will be attendees at a conference for small busines ...

Timnbspurban ownermanager ofnbspurbans motor court in

Tim Urban, owner/manager of Urban's Motor Court in Key West, is considering outsourcing the daily room cleanup for his motel to Duffy's Maid Service. Tim rents an average of 50 rooms for each of 365 nights (365 × 50 equa ...

1 find the greatest common divisor of 234 and 1242 find r

1. Find the greatest common divisor of 234 and 124. 2: Find r and s such that 8,092r + 1,111s = 1. 3: Find a counterexample to the claim that if the greatest common divisor of a and b is not 1, there exists a unique r an ...

Suppose xyz software company has a new application

Suppose XYZ Software Company has a new application development project, with projected revenues of $1,200,000. Using the following table, calculate the ARO and ALE for each threat category that XYZ Software Company faces ...

Verify that eulers theorem holds in zm m 69 for all

Verify that Euler's Theorem holds in Zm, m = 6,9, for all elements a for which gcd(a,m) = 1. Also verify that the theorem does not hold for elements a for which gcd(a,m) ≠ 1. For the affine cipher in Chapter 1 the multip ...

In an rsa digital signature scheme bob signs messages xi

In an RSA digital signature scheme, Bob signs messages xi and sends them together with the signatures si and her public key to Alice. Bob's public key is the pair (n,e); her private key is d. Oscar can perform man-in-the ...

1 can an snmp message reference a leaf node in the mib tree

1. Can an SNMP message reference a leaf node in the MIB tree? Explain. 2. Assume a manageable object has only three simple variables. How many leaves can be found in the MIB tree for this object? 3. Assume a manageable o ...

  • 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