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+...

Extracted text: 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: (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


Extracted text: 2. Using the graph below: (i) Draw the adjacency list (ii) Perform a breadth first search (BFS) and a depth first search (DFS) using A as your source. (iii) Derive the BFS tress diagram b) 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?