3. a) Using the Handshaking Principle, determine the number of edgesof a graph with fourteen (14) vertices and each with degree six (6)?b) Prove using method of induction for all n21P(n):1-2:3+ 2-3-4 +.+ n(n +1)(n + 2) = –n(n+1)(n + 2)(n + 3) ?4. a) Use the Laws of Algebra of sets and Logic to prove that:(i)P →Q is logically equivalent to (¬ P v Q)?Find the negations of P→Q?(iii) Using Truth Table that: P+→ Q =(P→Q)^(Q→ P)?(ii)b) Determine the duality of the Boolean equations(i)(a . 1)+ (0+ a) = 0(ii)a . (a +b) = a . b(iii)a+ (a. b) = a +b(iv)(a+1). (a+0) = a 2.Using the graph below:(i)Draw the adjacency list(ii)Perform a breadth first search (BFS) and a depthfirst search (DFS) using A as your source.(iii) Derive the BFS tress diagramb) Given two primes p= 11, q = 3 and e = 17. Determine the following:The totient function ( )?Show that the GCD ( 0 , e) = 1 and determine d?(iii) State the Public and Private key?(i)(ii)(iv) Starting with letter “A" as "0", encrypt the word GO?(v)State and explain one property of the decryption key d?

3 a. Given: Number of vertices -14 Degree of each vertex = 6 Number of edges =? The Handshaking…

3. a) Using the Handshaking Principle, determine the number of edges of a graph with fourteen (14) vertices and each with degree six (6)? b) Prove using method of induction for all n21 P(n):1-2-3+2-3-4+. + n(n + 1)(n + 2) = –n(n +1)(n + 2)(n + 3) ? 4. a) Use the Laws of Algebra of sets and Logic to prove that: P→Q is logically equivalent to (¬PVQ)? Find the negations of P→Q? (iii) Using Truth Table that: P+ Q =(P→Q)^(Q→ P)? b) Determine the duality of the Boolean equations (a . 1)+ (0+a) = 0 a . (a +b) = a . b (i) (ii) (i) (ii)

3. a) Using the Handshaking Principle, determine the number of edges of a graph with fourteen (14) vertices and each with degree six (6)? b) Prove using method of induction for all n21 P(n):1-2-3+2-3-4+. + n(n + 1)(n + 2) = –n(n +1)(n + 2)(n + 3) ? 4. a) Use the Laws of Algebra of sets and Logic to prove that: P→Q is logically equivalent to (¬PVQ)? Find the negations of P→Q? (iii) Using Truth Table that: P+ Q =(P→Q)^(Q→ P)? b) Determine the duality of the Boolean equations (a . 1)+ (0+a) = 0 a . (a +b) = a . b (i) (ii) (i) (ii)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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