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Assignment No. 1

Semester: Spring 2015

Data Communication - CS601


Total Marks: 12


Due Date: 25/05/2015




To have the understanding of signals and their encoding schemes.


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Consider a computer network of a social networking web site in which 7 routers are connected with each other using a dedicated wired point to point link. Each link is of 5 meters and cost of wire is 100 PKR per meter.


In view of the above scenario answer the following questions and provide yours to-the-point answers in respective tables.


  1. What will be the total number of links before and after adding this new router?


No. of Links before adding new router

No. of Links after adding new router


Final Answer




Final Answer




  1. What will be the total cost of wire before adding this new router and after adding this router?


Total cost of wire before adding new router

Total cost of wire after adding new router


Final Answer




Final Answer





Note: Give you solution with all relevant calculations in given tables.











Wish You All The Best



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Assignment # 1 Mth202

 Spring 2015

                                                                                                            Maximum Marks: 20

                                                                                                            Due Date: 27th May,2015




Please read the following instructions before attempting the solution of this assignment:


 •     To solve this assignment, you should have good command over 01-10 lectures.

In order to solve this assignment you have strong concepts about following topics:

ü  Logic, laws of logic and its application

ü  Truth tables and conditional statements

ü  Set theory

ü  Venn diagram and its applications

Try to get the concepts, consolidate your concepts and ideas from these questions which you learn in these lectures. You should concern the recommended books for clarification of concepts.

  •    Upload assignments properly through LMS. No Assignment will be accepted through email.

  •    Write your ID on the top of your solution file.

  • Do not use colorful back grounds in your solution files.
  • Use Math Type or Equation Editor etc. for mathematical symbols and equations.
  • You should remember that if we found the solution files of some students are same then we will reward zero marks to all those students. Therefore, try to make solution by yourself and protect your work from other students, otherwise you and the student who send same solution file as you will be given zero marks.
  • Avoid copying the solution from book (or internet); you must solve the assignment yourself.
  • Also remember that you are supposed to submit your assignment in Word format any other like scan images, HTML etc. will not be accepted and we will give zero marks correspond to these assignments.
  • You are directed to carefully see your section’s assignment with the Section Incharge name mentioned on it and attempt your relevant assignment. Moreover you will be awarded zero marks if you will submit assignment other than your section.


Section 1

Section Incharge Name:-  Sadaf Munir


Question: 1(a)                                                                                                         Marks:05


Construct a truth table for the following proposition:


Question: 1(b)                                                                                                         Marks:05


Write each of these propositions in the form “p if and only if q” in English.

1. If you watch television your mind will decay, and conversely.

2. The trains run late on exactly those days when I take it.

3. If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside.

Question: 2                                                                                                      Marks:10


Show that if A, B, and C are sets, then

(a)   by showing each side is a subset of the other side

(b)   by using a membership table.


Section 2

Section Incharge Name:-  Saima Shafi


Question: 1                                                                                                          Marks:07+06

If  then by using the laws of logic show that.

Also construct a truth table for .

Note: Please mention each law of logic properly which you have used in your solution.


Question: 2                                                                                                               Marks:04+03

There are 100 software developers in a software company, in which 75 professionals are expert to developing computer programs, 45 are expert in application soft wares, and 35 keep know how both in computer programs and application softwares.Using the Venn diagrams show that:

(a) How many professional are skilled either a computer programs or an application software?

(b) How many professional did not well either a computer programs or application software?


Section 3

Section Incharge Name:-  Jamshaid Nasir


Question: 1                                                                                                          Marks:10


Use truth table to test the validity of the following argument.

If you invest in the HBFC, then you get rich.

You didn’t invest in the HBFC.

Therefore, you didn’t get rich.                                   


Question: 2                                                                                                         Marks:10

Prove that the statement  is tautology.


Section 4

Section Incharge Name:-  Asmat Batool


Question 1;                                                                                                    Mark:4+6=10                       


Name the laws of logic used in the following statements:

(i)                 (~p→q) Ù(q→p) ≡ (pÚq) Ù(~qÚp)

(ii)               r ↔ s ≡ s ↔ r

(iii)             (~(~q)) Ú(pÙr) ≡ q Ú(pÙr)

(iv)             (pÚp) Ú(~r) ≡ p Ú (~r)




(i)Use De Morgan’s Law on q Ù(~(~pÚq)).                        

(ii)Use Distributive Law on rÚ(~sÙs)                                                      

(iii)Use Associative Law on the (~qÚp) Ú~p                           




Question 2;                                                                                                         Marks: 8

With the help of Membership table show that (A È B) – C= (A – C) È ( B – C)


Question 3;                                                                                                         Marks: 2

Convert the following statement in mathematical expression.

 “If the rain destroys the crops or the fire destroys the crops, then the government compensates the farmers”.




No of routers = n = 7

According to formula 

No. of links = n(n-1)/2

putting the value of n

No. of links = 7(7-1)/2

No. of links = 21

By Adding One more router 


Number of routers = n = 8

According to formula,

No. of links = n(n-1)/2

Putting the value of n:

No. of links = 8(8-1)/2

No. of links = 56/2

No. of links = 28


Now As we know that cost of wire is 100 PRK per meter

So that , 

cost of link(5m wire)  = 5*100

                              = 500

cost of 21 links = 21*500

cost of 21 links = 10500PKR

and also 

cost of 28 links = 28*500

cost of 28 links = 14000PKR

No. of Links before adding new router
Calculation Final Answer
7(7-1)/2 21
No. of Links after adding new router
Calculation Final Answer 
8(8-1)/2 28

Total cost of wire before adding new router
Calculation Final Answer
21*5*100 10500
Total cost of wire after adding new router
Calculation Final Answer
28*5*100 14000
Can anyone tell if my answers are correct or wrong?

2nd Question is wrong correct is like this
Total cost of wire before adding new router
Calculation Final Answer
21*5*100 10500
Total cost of wire after adding new router
Calculation Final Answer
28*5*100 14000


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