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Virtual University of Pakistan
Spring 2017
1
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. Following rules 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 due date will be accepted.
Virtual University of Pakistan
Spring 2017
2
Answer the following questions in your own words. Plagiarism will be checked for
each question. Marks will be awarded on the basis of answer and plagiarism report.
Question 1 (6 + 6 + 6 = 18 Marks)
Prove that  B →  (A  (A → B)) by
a) Logical equivalence
b) Rules of inference
c) Contradiction
Question 2 (12 Marks)
Show by mathematical induction that any amount in cents ≥ 18 cents can be obtained
using 4 cents and 7 cents coins only.
Question 3 (10 Marks)
Use Mathematical Induction to prove
1
2 ( 1)
i m
i
i m m


   .
Question 4 (10 Marks)
Suppose sequence, b0, b1, b2, . . ., satisfies recurrence relation
Then find explicit formula for b0, b1, b2, . . ., using characteristic equation of the above
recursion.
with initial condition : b 2 and 6
6 9 2
0 1
1 2
 
     
b
b b b k k k k

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