ICS 6D
Due: Friday, April 10, 2015, 2:00PM
Homework 1
Instructor: Sandy Irani
1. The propositional variables p, q, and r have the following truth values:
p=T
q=F
r=F
What is the truth value of the following compound propositions:
(a) (p q) r
(b) (r p q
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Name
Student ID
Score
Test 1
ICS 6D
Summer Session I
Wednesday, July 2, 2014
Instructor: Sandy Irani
2
1. (6 points)
(a) Fill in the truth table below:
p
q
T
T
T
F
F
T
F
(p q) p
F
(b) Is it a tautology? Why or why not?
(c) Is it a contradction? Why or why
Chapter 1 - Logic
Section 1.1 - Propositions and logical operations
Logic is the study of formal reasoning. A statement in a spoken language, such as in English, is often
ambiguous in its meaning. By contrast, a statement in logic always has a well-define
file:/C|/Documents%20and%20Settings/Linda%20Grauer/My%20Documents/Dolores/UC%20Irvine-Harvest/ICS%206D/hmw2.htm
Homework 2: Due *Monday*, October 15, at *2pm*. (See the class webpage for how to drop off your homeworks.) All exercises are from Rosen:
I&C SCI GD LEC A (36540)
Quiz 1 (Fall Qtr 2014) - LETTER SIZE
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Assigned Seat#:
Instructions to Instructor:
Do not alter this coversheet in ANY way. Substantial delays and additional fees may apply.
lggtrugtions to Student:
1. Clea
Chapter 3 - Sets
Section 3.1 - Sets and subsets
Sets play an important role in almost every area of mathematics, including discrete math. Set theory is
a well-developed branch of mathematics in its own right, most of which is beyond the scope of this
mate
ICS 6D
Due: Wednesday, April 13, 2016, 3:00PM
Homework 2
Sections 8.1-8.5
Instructor: Sandy Irani
1. Give the first six terms of the following sequences. You can assume that the sequences start with an
index of 1.
(a) The nth term is d ne.
(b) The nth ter
Name
Student ID
Score
Test 3
ICS 6D
Summer Session I
Wednesday, July 16, 2014
Instructor: Sandy Irani
2
1. (2 points) Compute 837 mod 11.
2. (2 points) Give the base-3 representation of (77777777)9 . (Hint, start with the base-3 representation
of (7)9 . T
ICS 6D
Due: Monday, June 30, 2014
Homework 2
Instructor: Sandy Irani
1. Dene the following sets as:
A = cfw_x Z : x is an integer multiple of 3
B = cfw_x Z : x is perfect square
C = cfw_4, 5, 9, 10
D = cfw_2, 4, 11, 14
E = cfw_3, 6, 9
F = cfw_4, 9
ICS 6D
Due: Monday, July 7, 2014
Homework 3
Instructor: Sandy Irani
1. Give the rst six terms of the following sequences. You can assume that the sequences start with an
index of 1. Logs are base 2.
(a) The nth term is log n .
(b) The nth term is 2
log n
Chapter 7 - Computation
Section 7.1 - An introduction to algorithms
Suppose you were given a list of five numbers and asked to find the smallest one. You would probably
only require a quick glance at the list of numbers to find the smallest one. Suppose,
Chapter 9 - Integer Properties
Section 9.1 - The Division Algorithm
The first mathematical objects most people encounter are integers. Integers are a natural component
of everyday life and easy to understand. Even so, some of the deepest mathematical myst
ICS 6D
Due: Wednesday, May 18, 2016, 3:00PM
Homework 7
Instructor: Sandy Irani
Sections 10.5-10.7
Leave your answer for the questions below as an arithmetic expression, including the P (n, k) or
notation. You do not have to compute a final numeric value.
ICS 6D - Winter 2015
Homework for Week 2
Covers Sections 7.1, 7.2
1. Give a recursive denition for strings of properly nested parentheses and curly braces. For example
(cfw_)cfw_() is properly nested but (cfw_) is not.
2. Let B = cfw_0, 1. In lecture, we
Name
Student ID
Score
Test 2
ICS 6D
Summer Session I
Wednesday, July 2, 2014
Instructor: Sandy Irani
2
1. (4 points) Express the following sum using summation notation:
(a) The sum of the positive even integers, less than or equal to 200.
(b) 32 + 31 + 30
Chapter 10 Advanced Counting
Chapter 10.1 Pigeonhole Principle
Chapter 10.3 Linear recurrence relations
Recurrence relation: specifies how to determine each number as a function of the numbers that
occur earlier in the sequence.
Initial Conditions: specif
ICS 6D Chapter 9-10
Chapter 9 Introduction to Counting
9.1 Counting Basics
Bijection Rule: provides a way to count one set in relation to another set. Let A and B be two
finite sets. If there is a bijection from A to B, then |A| = |B|. Note: |A| means car
Name
Student ID
Score
Test 4
ICS 6D
Summer Session I
Wednesday, July 23, 2014
Instructor: Sandy Irani
2
1. (6 points) There are 10 avors of taffy sold at the candy store. There is a plenitful supply of each
avor.
(a) How many ways are there to select 50 p
1.1-1.5, 2.1-2.3, 3.1, 3.4, 7.1- 7.3, 7.4,) 8.1-8.2, 8.3-)8.6, 9.1-9.4, 10.1-10.2, 9.5, 9.6, 10.3
ICS 6D Chapter 3: Functions
3.1 Properties of Functions
-In a function f the domain is X and x X; the target is Y and y Y
-f: X Y for function f, X maps to Y
Ch. 2: The Upheaval in Christendom, 1300-1560
(pp. 46-105)
Intro: Societies in transition from a traditional to a modernized form of society tend to become secularized-developing activities outside of the sphere of religion. Latin Christendom was the firs
ICS 6D
Due: Friday, June 5, 2015, 2:00PM
Homework 9
Section 9.6, June 1 Reading
Instructor: Sandy Irani
Leave your answer for the questions below as an arithmetic expression, including the P (n, k) or
notation. You do not have to compute a final numeric v
ICS 6D
Due: Friday, May 22, 2015, 2:00PM
Homework 7, Part II
Instructor: Sandy Irani
Covers May 18 reading
This is the second part of homework 7. Please submit your solutions to both parts I and II stapled
together in one submission. It will be graded as
ICS 6D
Due: Friday, May 15, 2015, 2:00PM
Homework 6
Instructor: Sandy Irani
Sections 9.1-9.4
Leave your answer for the questions below as an arithmetic expression, including the P (n, k) or
notation. You do not have to compute a final numeric value.
n
k
1
1
INDUCTION AND
RECURSION
Chapter 8 [Sections 1 through 11]
2
SECTION 8.1:
SEQUENCES
3
Sequences
A sequence is a special type of function in which the
domain is a consecutive set of integers:
a(0)=2, a(1) = 3, a(2) = 5, a(3) = 7, a(4) = 11
In a sequence