TERMS (Exam)
The Digital Design Audience
Implied designee
Real designee
Target Market
Persona
The Principles of Design 1
Design
Design Principle
Satisficing
80/20 rule
Affordance
Confirmation
Hierarchy of Needs
Wayfinding
Flexibility-Usability Tradeoff
En

= z) (T (x, y) T (z, y) e) xzy(T
(x, y) T (z, y) f ) xzy(T (x, y) T
(z, y) 8. Let Q(x, y) be the statement
student x has been a contestant on quiz
show y. Express each of these sentences
in terms of Q(x, y), quantifiers, and logical
connectives, where the

least 60 course hours, or at least 45
course hours and write a masters thesis,
and receive a grade no lower than a B in
all required courses, to receive a masters
degree. d) There is a student who has
taken more than 21 credit hours in a
semester and rece

a student none of whose friends are also
friends with each other. Translating
English Sentences into Logical
Expressions In Section 1.4 we showed
how quantifiers can be used to translate
sentences into logical expressions.
However, we avoided sentences wh

Introduction In Section 1.4 we defined the
existential and universal quantifiers and
showed how they can be used to
represent mathematical statements. We
also explained how they can be used to
translate English sentences into logical
expressions. However,

domain consist of the students in your
class and second, let it consist of all
people. a) Everyone in your class has a
cellular phone. b) Somebody in your class
has seen a foreign movie. c) There is a
person in your class who cannot swim. d)
All students

the statements xyzQ(x, y, z) and
zxyQ(x, y, z), where the domain of all
variables consists of all real numbers?
Solution: Suppose that x and y are
assigned values. Then, there exists a real
number z such that x + y = z.
Consequently, the quantification
xy

Let Q(x) be the statement x + 1 > 2x. If
the domain consists of all integers, what
are these truth values? a) Q(0) b) Q(1) c)
Q(1) d) xQ(x) e) xQ(x) f ) xQ(x) g)
xQ(x) 13. Determine the truth value of
each of these statements if the domain
consists of all

student in your class who has chatted
with everyone in your class over the
Internet. n) There are at least two
students in your class who have not
chatted with the same person in your
class. o) There are two students in the
class who between them have cha

= 1) P (x) d) x(x 0) P (x) e)
x(P (x) x(x < 0) P (x) 21. For
each of these statements find a domain
for which the statement is true and a
domain for which the statement is false.
a) Everyone is studying discrete
mathematics. b) Everyone is older than 21
y

has asked every faculty member a
question. g) There is a faculty member
who has asked every other faculty
member a question. h) Some student has
never been asked a question by a faculty
member. 12. Let I (x) be the statement x
has an Internet connection a

of z that satisfies the equation x + y = z for
all values of x and y. Translating
Mathematical Statements into Statements
Involving Nested Quantifiers
Mathematical statements expressed in
English can be translated into logical
expressions, as Examples 68

system errors have been detected. c) The
file system cannot be backed up if there is
a user currently logged on. d) Video on
demand can be delivered when there are
at least 8 megabytes of memory available
and the connection speed is at least 56
kilobits p

statement x knows the computer
language C+. Express each of these
sentences in terms of P (x), Q(x),
quantifiers, and logical connectives. The
domain for quantifiers consists of all
students at your school. a) There is a
student at your school who can spe

DAC 201 Essay Assignment
Introduction
The module Designing Logos for the Food Industry is a best practice
module that functions to help designers articulate the best use of text, shapes,
colours, and space to design a logo that is most effective to attrac

Topic: Designing logos for the food industry.
Kind of module: This module is a best practice, which involves combining text,
shapes, and colour to create company brand logos. My instructional module will
explore successful company brand logos and how to d

The Digital Design Audience
Implied designee design that projects for an end user, someone who is
looking for an inexpensive lightweight tool that will be used occasionally,
second is someone who is willing to pay for comport and aesthetic appeal
o Who yo

Name: Vivian Diec
Topic: Designing logos for the food industry.
Kind of module: This module is a best practice, which involves combining text,
shapes, and colour to create company brand logos. My instructional module will
explore successful company brand

y = y + x. This has the same meaning as
the statement For all real numbers x, for
all real numbers y, x + y = y + x. That is,
xyP (x, y) and yxP (x, y) have the
same meaning, P1: 1/1 P2: 1/2 QC: 1/1
T1: 2 CH01-7T Rosen-2311T MHIA017Rosen-v5.cls May 13, 20

computer and x and y are friends. In other
words, every student in your school has a
computer or has a friend who has a
computer. EXAMPLE 10 Translate the
statement xyz(F (x, y) F (x, z) (y
= z) F (y,z) P1: 1/1 P2: 1/2 QC: 1/1
T1: 2 CH01-7T Rosen-2311T MH

succinctly as The product of a positive
real number and a negative real number is
always a negative real number.
THINKING OF QUANTIFICATION AS
LOOPS In working with quantifications of
more than one variable, it is sometimes
helpful to think in terms of n

existential and universal quantifiers!
Example 4 illustrates that the order in
which quantifiers appear makes a
difference. The statements yxP (x, y)
and xyP (x, y) are not logically
equivalent. The statement yxP (x, y) is
true if and only if there is a

inverse. (A multiplicative inverse of a real
number x is a real number y such that xy
= 1.) P1: 1/1 P2: 1/2 QC: 1/1 T1: 2 CH017T Rosen-2311T MHIA017-Rosen-v5.cls
May 13, 2011 15:27 1.5 Nested
Quantifiers 61 Solution: We first rewrite
this as For every rea

conjunctions, and negations. a) xP (x) b)
xP (x) c) xP (x) d) xP (x) e) xP
(x) f ) xP (x) P1: 1/1 P2: 1/2 QC: 1/1
T1: 2 CH01-7T Rosen-2311T MHIA017Rosen-v5.cls May 13, 2011 15:27 54 1 /
The Foundations: Logic and Proofs 19.
Suppose that the domain of the

or 2, y = 0 or 1, and z = 0 or 1. Write out
these propositions using disjunctions and
conjunctions. a) yQ(0, y, 0) b) xQ(x, 1,
1) c) zQ(0, 0, z) d) xQ(x, 0, 1) P1:
1/1 P2: 1/2 QC: 1/1 T1: 2 CH01-7T
Rosen-2311T MHIA017-Rosen-v5.cls May
13, 2011 15:27 1.4 P

respectively. Give a Prolog rule to define
the predicate sibling(X, Y ), which
represents that X and Y are siblings (that
is, have the same mother and the same
father). 58. Suppose that Prolog facts are
used to define the predicates mother(M, Y
) and fath

(x). We obtain the logically equivalent
expression xy(F (x) P (x) M(x,
y). EXAMPLE 12 Express the
statement Everyone has exactly one best
friend as a logical expression involving
predicates, quantifiers with a domain
consisting of all people, and logical

such that 0 < |x a| < and |f (x) L| .
Exercises 1. Translate these statements
into English, where the domain for each
variable consists of all real numbers. a)
xy(x < y) b) xy(x 0) (y 0)
(xy 0) c) xyz(xy = z) 2. Translate
these statements into English,

science major. c) There is a student in the
class who is neither a mathematics major
nor a junior. d) Every student in the class
is either a sophomore or a computer
science major. e) There is a major such
that there is a student in the class in every
year

is usually preferable. Negating Nested
Quantifiers Statements involving nested
quantifiers can be negated by successively
applying the rules for negating statements
involving a single quantifier. This is
illustrated in Examples 1416. EXAMPLE
14 Express th