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Georgia Tech | CS 1155

#### 25 sample documents related to CS 1155

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
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

• Georgia Tech CS 1155
CS 1155: Understanding and Constructing Proofs Home work 1 Spring 1999 Due: Friday, April 9, 1999 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. b 10 points Prove that 5 is irrational.

• Georgia Tech CS 1155
CS 1155: Understanding and Constructing Proofs Home work 6 Due: Friday, May 21, 1999 1. 10 points Exercises 4.2, problem 18, page 211 of the text. 2. 10 points Exercises 4.2, problem 22, page 211 of the text. 3. 15 points Exercises 4.4, problem 8, p

• Georgia Tech CS 1155
CS 1155: Understanding and Constructing Proofs Home work 4 Spring 1999 Due: Friday, May 7, 1999 1. 10 points Exercises 2.5, problem 9 b and c, page 118 of the text. 2. 15 points Exercises 2.5, problem 10 a, b, and c, page 118 of the text. 3. 15 p

• Georgia Tech CS 1155
CS 1155 HW#2 Sample Solutions 1. Prove the distributive law A(BC)=(AB)(AC). Proof: We can use Venn diagrams to solve this problem. Alternatively, we can first show A(BC)(AB)(AC), then we show A(BC)(AB)(AC). To show A(BC)(AB)(AC), we consider an eleme

• Georgia Tech CS 1155
CS1155 Homework 3 Solutions 1. Let p1, p2, ., pn be n propositions for n >= 2. Write a compound proposition that is true when: a. more than half of the propositions are true; Define S = { p1, p2, ., pn}. P(S) is the power set of S. One way to simplif

• Georgia Tech CS 1155
CS 1155: Understanding and Constructing Proofs Home work 5 Spring 1999 Due: Friday, May 14, 1999 1. 10 points Exercises 3.5, problem 5 b, page 174 of the text. 2. 10 points Exercises 3.5, problem 18, page 176 of the text. 3. 15 points Let A be a

• Georgia Tech CS 1155
CS 1155 HW 5 Sample Solutions Question 1. (10points) Exercises 3.5, problem 5(b), page 174 of the text If G and H are both graphs with vertex set {1, 2, , n}, we say that G is isomorphic to H, and write G H, in case there is a way to label the vertic

• Georgia Tech CS 1155
CS 1155 Spring 1999 HW#7 Sample Solutions 1. Consider the following recurrence equation: sn = 6sn1 11sn2 +6sn3, with s0 = 3, s1 = 6, and s2 = 14. (a) (5 points) What is the characteristic equation of this recurrence? Solution: It is reasonable to ho

• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7

• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7

• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7

• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7

• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7

• Georgia Tech CS 1155
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• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7

• Georgia Tech CS 1155
%! /TeXDict 200 dict def TeXDict begin /Mtrx matrix def /@start { /StartTime usertime def vmstatus pop /@VMused exch def pop 72 720 translate } def /@letter { /letter where { pop letter 72 720 translate } if } def /@legal { /legal where { pop legal 7