C241 Homework 1
Spring 2009
Solution Set
Assigned: Jan. 14, 2009
Due: Jan. 23, 2009
1. Write out truth tables for the following logical statements. (Hint: You
may wish to include intermediate expressions in your truth table for
simplicity in evaluating th
C241 Homework 5
Assigned: Mar. 2, 2009
Due: Mar. 9, 2009
1. (a) Prove by induction that n < 2n for all natural numbers n, where
n 2. Remember that 2n+1 = 2(2n ) = 2n + 2n .
n
2i = 2n+1 1 for all natural numbers
(b) Prove by induction that
i=0
n. (That is,
C241 Homework 6
Assigned: Mar. 11, 2009
Due: Mar. 23, 2009
1. Use the language P dened below to answer the following questions.
P cfw_(, )+ (P is a language in which every string contains only parentheses, and at least one parenthesis.)
P:
i. () P
ii. If
C241 Homework 9
Assigned: Apr. 24, 2009
Due: May 1, 2009
1. Give a representation of the following graph as:
(a) An adjacency list
(b) A 0-1 matrix
a
c
b
d
2. (a) The following graph contains undirected edges with distance weights.
Illustrate, step by ste
C241 Homework 3
Assigned: Feb. 9, 2009
Due: Feb. 18, 2009
1. Answer the following questions briey and in your own words.
(a) What is an open statement?
(b) What is the universe of discourse?
(c) Write an open statement with two variables and identify the
C241 Homework 8
Assigned: Apr. 16, 2009
Due: Apr. 22, 2009
As we have seen, a tree is a structure with nodes and edges. Each
node is connected to 0 or more child nodes by one edge per child. Trees
are useful representing many dierent kinds of information,
CSCI-C 241 Homework #2
Instructor: Wennstrom
Assigned Tuesday, September 1st, 2015
Due Tuesday, September 8th, 2015
1. (16 points) Answer the following questions. Justify your answers with an truth assignment or an entire table if appropriate. (For exampl
CSCI-C 241 Homework #3
Instructor: Wennstrom
Assigned Tuesday, September 8th, 2015
Due Tuesday, September 15th, 2015
1. (6 points) Give the truth trees for the following formulas.
(a) A (B C) A
Solution:
A (B C) A X
(B C) A X
A X
A
(B C) X
A
BC X
B
C
(b
C241 Homework 1
Spring 2009
Assigned: Jan. 14, 2009
Due: Jan. 23, 2009
1. Write out truth tables for the following logical statements. (Hint: You
may wish to include intermediate expressions in your truth table for
simplicity in evaluating the overall sta
C241 Homework 7: Solutions
PLEASE DO THIS ASSIGNMENT ON A SEPARATE PIECE OF PAPER.
1) The following are mistakes that often show up in numerical induction
proofs. Clearly describe what is wrong with each one.
1) The following are mistakes that often show
C241 Homework 3
Assigned: Feb. 9, 2009 Due: Feb. 16, 2009
1. Answer the following questions briefly and in your own words. (a) What is an open statement? A statement with at least one free variable (a variable which appears outside the scope of a quantifi
C241 Homework 5
Assigned: Mar. 2, 2009
Due: Mar. 9, 2009
1. (a) Prove by induction that n < 2n for all natural numbers n, where
n 2. Remember that 2n+1 = 2(2n ) = 2n + 2n .
First, we use our base case to prove that the rst property holds
for the rst eleme
C241 Homework 6
Assigned: Mar. 11, 2009
Due: Mar. 23, 2009
1. Use the language P dened below to answer the following questions.
P cfw_(, )+ (P is a language in which every string contains only parentheses, and at least one parenthesis.)
P:
i. () P
ii. If
C241 Assignment 7
Assigned: Mar 23, 2009
Due: Mar. 30, 2009
Notational convention for this solution: f (n) O(g (n) f (n) Cg (n)
for some positive constant coecient C and all n greater than some positive
constant N .
1. Label the following statements as tr
C241 Homework 8
Assigned: Apr. 16, 2009
Due: Apr. 22, 2009
As we have seen, a tree is a structure with nodes and edges. Each
node is connected to 0 or more child nodes by one edge per child. Trees
are useful representing many dierent kinds of information,
C241 Homework 9
Assigned: Apr. 24, 2009
Due: May 1, 2009
1. Give a representation of the following graph as:
a
c
(a) An
a
b
c
d
b
d
adjacency list
bc
acd
abd
bc
(b) A 0-1 matrix
abc
a011
b101
c110
d011
d
0
1
1
0
2. (a) The following graph contains undirec
C241 Exam 2 Solution Problem 2
Note: Theres a lot of explanation in this solution. This is to clarify the
issues involved and would not be a required part of any answer given on the
exam.
2.
E:
i.
ii.
iii.
If n is a positive integer then n is in E (i.e.,
CSCI-C 241 Homework #1
Instructor: Wennstrom
Assigned Wednesday, August 26th, 2015
Due Tuesday, September 1st, 2015
1. (22 points) Which of the following are propositions? If you think it is a proposition,
write proposition and then state whether you thin