Assigned Wednesday, January 20, 2016
Due Monday, February 1, 2016
CSCI-C 241 Homework #2
Instructor: Dirk Van Gucht
1. (10) Let P and Q be propositions. Show that P Q if and only if (P Q) Q.
2. (5) Solve Exercise 31.a in Chapter 1 in your textbook.
3. (5)

CSCI-C 241 Homework #6
Instructor: Dirk Van Gucht
Assigned Tuesday, March 22, 2016
Due Monday, March 28, 2016 (IN CLASS)
Each problem or subproblem is worth 10 points.
Notes: Instead of using the notation x A, I will use the shorter notation A(x) and inst

CSCI-C 241 Homework #5
Instructor: Dirk Van Gucht
Assigned Monday, March 1, 2016
Due Wednesday, March 9, 2016 (IN CLASS)
Each problem or subproblem is worth 10 points.
Most questions come from or are based on problems from the excellent book Introduction

CSCI-C 241 Homework #3
Instructor: Dirk Van Gucht
Assigned Monday, February 1, 2016
Due Monday, February 8, 2016
For this homework you should consult the Lecture Notes on Propositional Logic and the
document Laws-And-Inference-Rules which I both posted.
1

Assigned Thursday, April 14, 2016
Due Monday, April 25, 2016 (IN CLASS)
CSCI-C 241 Homework #9
Instructor: Dirk Van Gucht
Each problem or subproblem is worth 10 points.
1. Consider the following recurrence relation:
f (n)
=
=
0
f (n 1) + 3n2 3n + 1
if n =

Assigned Monday, Feb 15, 2016
Due Wednesday, Feb 24, 2016
CSCI-C 241 Homework #4
Instructor: Dirk Van Gucht
Each problem or subproblem is worth 10 points.
1. Solve Exercise 1.3.6 in your textbook.
See the question below.
2. Solve Exercise 1.3.6.a and 1.3.

CSCI-C 241 Homework #5
Instructor: Dirk Van Gucht
Assigned Monday, March 1, 2016
Due Wednesday, March 9, 2016 (IN CLASS)
Each problem or subproblem is worth 10 points.
Most questions come from or are based on problems from the excellent book Introduction

Assigned Thursday, April 14, 2016
Due Monday, April 25, 2016 (IN CLASS)
CSCI-C 241 Homework #9
Instructor: Dirk Van Gucht
Each problem or subproblem is worth 10 points.
1. Consider the following recurrence relation:
f (n)
=
=
0
f (n 1) + 3n2 3n + 1
if n =

CSCI-C 241 Homework #3
Instructor: Dirk Van Gucht
Assigned Monday, February 1, 2016
Due Monday, February 8, 2016
For this homework you should consult the Lecture Notes on Propositional Logic and the
document Laws-And-Inference-Rules which I both posted.
1

CSCI-C 241 Homework #1
Instructor: Dirk Van Gucht
Assigned Tuesday, January 12, 2016
Due Wednesday, January 20, 2016
1. Which of the following are propositions? If you think it is not a proposition, write not
a proposition and give a short reason why you

CSCI-C 241 Homework #7
Instructor: Dirk Van Gucht
Assigned Monday, March 29, 2016
Due Monday, April 4, 2016 (IN CLASS)
Each problem or subproblem is worth 10 points.
In this homework consider the following relations. Let P = cfw_Sam, Eric, N ick, Ann be
a

Assigned Wednesday, January 20, 2016
Due Monday, February 1, 2016
CSCI-C 241 Homework #2
Instructor: Dirk Van Gucht
1. (10)(*) Let P and Q be propositions. Show that P Q if and only if (P Q) Q.
Since P and Q are propositions, they are built from some atom

CSCI-C 241 Homework #7
Instructor: Dirk Van Gucht
Assigned Monday, March 29, 2016
Due Monday, April 4, 2016 (IN CLASS)
Each problem or subproblem is worth 10 points.
In this homework consider the following relations. Let P = cfw_Sam, Eric, N ick, Ann be
a

CSCI-C 241 Quiz #7
Instructor: Dirk Van Gucht
Thursday, April 21, 2016
This quiz concerns proofs by induction, i.e., proofs by mathematical induction, strong
mathematical induction, or structural induction. When I write Prove by induction that
I mean tha

CSCI-C 241 Homework #1
Instructor: Dirk Van Gucht
Assigned Tuesday, January 12, 2016
Due Wednesday, January 20, 2016
1. Which of the following are propositions? If you think it is not a proposition, write not
a proposition and give a short reason why you

CSCI-C 241 Quiz #6
Instructor: Dirk Van Gucht
Thursday, March 31, 2016
In this homework consider the following relations. Let P = cfw_Sam, Eric, N ick be a set
of persons and let C = cfw_Bloomington, Indy be a set of cities. Then, let knows, likes, and
re

CSCI-C 241 Homework #4
Instructor: Dirk Van Gucht
Assigned Monday, Feb 15, 2016
Due Wednesday, Feb 24, 2016
Each problem or subproblem is worth 10 points.
1. Solve Exercise 1.3.6 in your textbook.
2. Solve Exercise 1.3.6.a and 1.3.6.b in your textbook.
3.

CSCI-C 241 Quiz #4
Instructor: Dirk Van Gucht
Thursday, March 3, 2016
Make sure to indicate the inference rules and replacement laws that you used in your
proofs.
1. For this example we assume that we have the unary predicates greek(x), mortal(x) and
huma

CSCI-C 241 Quiz #5
Instructor: Dirk Van Gucht
Thursday, March 24, 2016
1. Let U = cfw_1, 2, 3, 4, 5, 6, 7 and let A = cfw_1, 2, 3, B = cfw_3, 4, 5, and C = cfw_6.
1. Determine the set A (B C).
Solution: We can see that (B C) = .
A (B C)
=
=
=
=
A (B C)
A

CSCI-C 241 Quiz #1
Instructor: Dirk Van Gucht
1. Translate the following sentences into propositional logic. Use the given
definitions for the atomic propositions.
F You have the flu.
I You miss your interview.
H You get hired.
(a) (5 points) You attend y

CSCI-C 241 Homework #8
Instructor: Dirk Van Gucht
Assigned Moday, March 29, 2016
Due Thursday, April 14, 2016 (In Discussion)
Each problem or subproblem is worth 10 points.
1. Let f and g be two one-to-one correspondences (bijections) from U to U. Prove t

CSCI-C 241 Quiz #2
Instructor: Dirk Van Gucht
February 4, 2016
For this quiz you can use the document Laws-And-Inference-Rules.
1. (10) Show that the Abjunction Law
(P Q) P Q
can be derived from the Fundamental Replacement Laws. You are not permitted to u

CSCI-C 241 Quiz #3
Instructor: Dirk Van Gucht
Thursday, February 11, 2016
Make sure to indicate the inference rules and replacement laws that you used in your
proofs.
1. Prove the following logical implication
(W X) Y, X W Y
1.
(W X) Y
premise
2.
X
premis

Assigned Tuesday, March 22, 2016
Due Monday, March 28, 2016 (IN CLASS)
CSCI-C 241 Homework #6
Instructor: Dirk Van Gucht
Each problem or subproblem is worth 10 points.
1. Let U = cfw_a, b, c, d, e, f and let A = cfw_a, b, c, d and B = cfw_c, d, e. Determ