APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER M.TECH DEGREE EXAMINATION, DECEMBER 2015
COMPUTER SCIENCE & ENGINEERING

(INFORMATION SECURITY/COMPUTER SCIENCE & ENGINEERING,'NETWORK
ENGINEERING)

0 1 (56101 MATHEMATICAL FOUNDATIONS OF COMPUTING SYSTEMS >
Max. Marks : 60 Duration: 3 Hrs
(Answer Any Two Questions From Each PART. All Questions Carry Equal
Marks)

1(8) Show that if n = ab , where a and b are positive integers , thenas'/norbs

un by contraposition. (3)

(b) Solve the recurrence relation ar-2ar.1 = (r+l) using characteristic root
method (3)

(c) Explain Branching -time logic. (3)

2(a) Prove by exhausting cases that 203 +3n ° +n is an even integer (3)

(b) Let HI = 1. 141/2, Hn- 14+1/2+...+1/n Prove thatHi=(n+1)Hn-n
for all +ve integers nzl (3)
(c) What is meant by adequate set of connectjves?Explain. (3)
3(a) Show that t/2 is irrational by giving a proof by contradiction (3)

(b)Solve the Fibonacci series an.Itan-2 ; 83,8171, using Generating

Functions.
(3)

(c) Briefly discuss Linear -time temporal Logic. (3)

(2 x 9= 18 marks)