CS 1155 Georgia Tech

CS1155 HW 8 Solutions 1. Consider the following recursive definition of a tree: [See hw assignment] a) (5 points) Draw the graph obtained by applying the recursive step three times starting from the basis. The tree is a complete binary tree. b) (10

CS 1155: Understanding and Constructing Proofs Home work 8 Due: Friday, June 4, 1999 1. Consider the following recursive de nition of a tree: Let r be a vertex. Then, the vertex set V = frg, and the edge set E = is a tree with root r and leaf set L

CS 1155: Understanding and Constructing Proofs Quiz 3 May 21, 1999 Solution sketch 1. 10 points Let be a nite alphabet. Say that a string x is related to a string y if length of x is equal to the length of y. This is an equivalence relation on . a

CS 1155 HW6 Sample Solutions 1. (10 points) Exercises 4.2, problem 18, page 211 of the text. Prove 1 + 2 + . + n = (1 + 2 + . n) , i.e., i = [ i]2 for all n in . Hint: 3 3 3 2 3 i=1 i=1 n n Use the identity in Example 2(b). Basis: n = 1: i = [i]2

CS 1155 HW4 Sample Solutions Exercises 2.5, problem 9 (b) and (c) Find a logical equivalence in Table 1 on page 84 from which the use of Substitution Rule (a) yields the indicated equivalence. (b) [p(q(rs)][(pq)(p(rs)] 1. comes from distributive la

Homework #1 Solutions Note: please always include the questions in your answers. 1. (a). (5 points) Prove that if a positive integer p is not a multiple of 5 then p2 is also not a multiple of 5. Proof by contradiction Suppose p2 is a multiple of 5, p

CS 1155: Understanding and Constructing Proofs Home work 7 Due: Friday, May 28, 1999 1. Consider the following recurrence equation: 1 = 6, and 2 = 14. s s sn Spring 1999 = 6 sn ,1 , 11 n,2 + 6 n,3 , with s s s0 = 3, a 5 points What is the ch

CS 1155: Understanding and Constructing Proofs Home work 3 1. 20 points Let 1 2 sition that is true when: a b c d p ; p ; ; pn Spring 1999 Due: Friday, April 30, 1999 n be propositions for n 2. Write a compound propo- more than half of the

CS 1155: Understanding and Constructing Proofs Home work 2 Spring 1999 Due: Friday, April 16, 1999 1. 10 points Prove the distributive law 3a, page 34 of the text. 2. 10 points Exercises 1.4, problem 13 a, b, d, e, and f page 39 of the text. 3. 5