CS702 Assignment 1 Solution and Discussion

CS702 – Advanced Algorithms Analysis and Design
Assignment 1
Instructions to Solve Assignments
The purpose of the assignments is to give students hands on practice. It is expected that students will solve assignments themselves. The Following rules that will apply during the evaluation of the assignment.
Cheating from any source will result in zero marks in the assignment.
Any student found cheating in any two of the assignments submitted during the course will be awarded
“F” grade in the course.
No assignment after the due date will be accepted.Answer the following questions in your own words. Plagiarism will be checked for each question. Marks will be awarded on the basis of the answer and plagiarism report.
Question No.1 (15 Marks)
Prove with the help of logical equivalence that the given proposition is a tautology. (p Λ q) v (~ p v ~( pq ))
Note: Show all the steps to get full marks
Question 2 (25 Marks)
Show by mathematical induction that any amount in cents ≥ n0 cents can be obtained using 8 cents and 9 cents coins only.
Note: First you will need to calculate n0.
Question No.3
Consider the recurrence
tn =n
(20) Marks
tn = 4tn1 11tn2
Find general solution of the recurrence above.
6tn3
otherwise
ifn=0,1,2

Q. 1 Solution:
Q. 2 Solution:
Q. 3 Solution: