Math 255 Handout 1.1 - 1.2, page 4
[cfw_(cfw_A B D) D (C A)] [A B]
A
(1)
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
B
(2)
T
T
T
T
F
F
F
F
T
T
T
T
F
F
F
F
D
(3)
T
T
F
F
T
T
F
F
T
T
F
F
T
T
F
F
C
(4)
T
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
AB
(5)
T
T
T
T
F
F
F
F
F
F
F
F
F
F
F
Math 255 Set Theory - - McLoughlins Class Functions, page 1 of 8
MATH 255 SET THEORY - DR. MCLOUGHLINS CLASS
HANDOUT 16
FUNCTIONS
Recall:
Let U be a well defined universe. Let V be the well defined universe, P(U).
Let A be a set. We considered theorems on
Math 255 Set Theory - - McLoughlins Class Ordinality page 1 of 6
MATH 255 SET THEORY - DR. MCLOUGHLINS CLASS
HANDOUT 15
AN INTRODUCTION TO ORDINALITY
Common custom characterises an ordinal number as an adjective which describes the numerical
position of a
Math 255 Set Theory - - McLoughlins Class The Pause, page 1 of 10
MATH 255 SET THEORY - DR. MCLOUGHLINS CLASS
HANDOUT 13
PAUSE TO CONSIDER WHERE WE ARE AND
FROM WHENCE WE CAME
We started this section of the course building from sets to the more general pr
Math 255 Set Theory - - McLoughlins Handy Dandy Methods Guide page 1 of 4
Dr. McLoughlins Methods of Proof Handy Dandy Guide
Direct Proof (1): To prove the implication (A B) from a set of premises cfw_say
H1 , H2 ,
. , Hk show that (A B) is provable as a
Set Theory Math 255
Handout 9
3.3
Algebra of Sets &
Laws to Memorise After You Have Proven Them
Mr. McLoughlin
Let U designate a well defined universe and A, B, and C sets within the universe.
Law of double complement
(A')' = A
Note: recall from logic: (
Set Theory Math 255
Handout 10
3.4
Collections, Generalised Union, and Generalised Intersection of
Sets
Dr. McLoughlin
Let U designate a well defined universe and A, B, and C sets within the universe.
For a generalised union or intersection of sets discu
Math 255 Handout 1.1 - 1.2, page 1
Set Theory Math 255 Handout 1.1 - 1.2
Some of the variations of the conditional and biconditional
(words and symbols)
Dr. McLoughlin
P Q, P Q , Q P , and Q P all mean If P, then Q.
Conditional
Now, the various mathematic
McLoughlin, Math 255 Handout 4, page 1
Set Theory Math 255
Handout 4
Standard Sets to Memorise
Dr. McLoughlin
N is the set of natural numbers, it is
cfw_1, 2, 3, 4, 5, . . .
N* is the set of natural numbers and the special number zero, it is cfw_0, 1, 2,
Math 255 Set Theory - - McLoughlins Class Generalised Point Method page 1 of 3
Math 255 Set Theory - Dr. McLoughlins Class
Handout 10
Generalised Point Method of Proof
Suppose we have a well defined universe U and sets X and Y that are subsets of the
univ
255 McLoughlin Handout 1.2 - 1.3
Set Theory Math 255 Handout 1.2 - 1.3
Important Principles and Rules to Memorise
Dr. McLoughlin
All prime statements P, Q, R, etc. are statements.
If P is a statement, then P is a statement.
If P and Q are statements, then
Math 255
Set Theory
Handout 3
Chapter 2
A Well Thought Out and Done Analytic Proof
(I hope)
Consider the following claim:
Claim 1 Let x, y and z be real numbers. If x > 0, y > 0, z > 0, and xy > z,
then x > z1/2 or y > z1/2
You must first READ the claim a
Math 255
Set Theory
Handout 2
Proof Versus Counterexample
There has been some confusion (as it has always been) between a proof and a counterexample.
Please refer to a text such as the text, "100% Mathematical Proof" (the old Math 180 text; or
another ava
Math 255 Set Theory - McLoughlins Class
The Axioms of Set Theory
Axiom 1) The Axiom of Extension Two sets are equal iff they have the same elements.
Axiom 2) The Axiom of Null There exists a set with no elements, call it .
Axiom 3) The Axiom of Pairing Gi