3.1 Set Denitions and Operations
hDef i A set is a collection of objects (called elements or members).
e.g., The elements of a football team are the players.
hN otei Its customary to use capital letters (such as A; B; C; S; X; Y ) to
designate sets and lo
4.1 Denitions, Diagrams, and Inverses
Q1: Can you give me an example of a function?
Q2: Does a function have to be able to be described by a formula?
hDef i The notation f : A ! B is used for a function, simply called f , with
a set of inputs A (called th
3.2 More Operations on Sets
Cartesian Products (p.198)
When we list the elements of a set, the order doesnt matter.
e.g., A = fx; yg = fy; xg:
hDef i The ordered pair (x; y) is a single element consisting of a pair of
elements in which x is the rst elemen
3.5 Logic Circuits
Data are stored and manipulated in a computer as binary numbers (i.e., as
strings of 0s and 1s). Each of the numbers in the string is referred to as a bit
(binary digit). Individual bits are represented by voltages, with two dierent
Based on our syllabus, I can say "If a student have 250 points or more, then
that student will get an A in this class."
Q1: Whats the unspoken domain D and quantier I have in mind?
Q2: Dene the predicates P (x) and Q(x) so that the senten
3.4 Boolean Algebra
One of the most remarkable properties of the study of mathematics is that
we frequently discover essentially identical patterns in widely diverse subject
Thm 2 (in Section 1.3) Let p, q, and r stand for any propositions. Let
2.6 Representations of Numbers
Decimal and Binary Numerals (p.150)
hDef i Given a positive integer X, the decimal representation (or base
ten representation) for X is a string that looks like dn dn 1
d2 d1 d0 , where
= dn 10n +
4.5 Equivalence Relations
Equivalence Relations and Partitions (p.314)
e.1 Let A = f1; 2; 3; 4; 5; 6g and a relation on A,
R = f(x; y) 2 A
y is eveng:
(a) Draw the one-set arrow diagram.
(b) Do you recognize any patterns or properties in the diagram
What does the word "predicate" mean in English?
In traditional grammar, a predicate is one of the two main parts of a sentence
the other being the subject, which the predicate modies. For the sentence
"Taiwan is not a part of China." Taiwan
1.3 Truth-tellers, Liars, and Propositional Logic
Lets solve some puzzles to get the fun started:)
e.1) Ex1(a) You come across two inhabitants of Smullyans Island. A
says "We are both telling the truth," and B says, "A is lying." Who if anyone