Discrete Mathematics UOG — University of Gujrat 2016

University of Gujrat

Final Term System Exam Fall 2016

Course Title: Discrete structure

Course code: CS-261

Total marks: 40

Time allowed: 110 min

Subjective

Part-1

Solve the following questions each of 5 marks. (5*5)

1. What are the contrapositive, the converse and the inverse of the conditional statement "The

home team wins whenever it is raining."

2. How can this English sentence be translated into a logical expression? "You cannot ride the

roller coaster if you are under 4 feet tall unless you are older than 16 years old."

3. Use De Morgan's laws to find the negation of the statement "Mei walks or takes the bus to

class."

4. Show that if n is a perfect square then n+2 is not a perfect square.

5. Find the sets A and B if A-B={1,5,7,8}, B-A={2,10}, and A ∩ B = {3,6,9}

Part-II

Attempt any 2 questions from the following. (7*10)

6. Find the length of shortest path between a and z in the given weighted graph.

7. Prove that 2 - 2*7 + 2*7^2 - ... + 2(-7)^n = (1-(-7)^(n+1))/4 whenever n is a nonnegative integer.

8. Show that if n is an odd integer, then there is a unique integer k such that n is the sum of k-2

and k+3.

Part-3

Attempt any one question from the following. (1*5)

9. Find ∪ Ai and ∩ Ai if for every positive integer i, Ai = (-i,

i)

10. Find at least three different sequences beginning with the terms 1, 2, 3 whose terms are

generated by a simple formula or rule.