5.15. Valid; the conclusion that is desired states that b is smaller than c. The first premise states that b is
a tetrahedron and the second says that c is a cube. Since the last premise is a disjunct
40. This argument is valid.
A
T
T
T
T
F
F
F
F
C
T
T
F
F
T
T
F
F
D
T
F
T
F
T
F
T
F
~
F
F
F
F
T
T
T
T
A
T
T
T
T
F
F
F
F
(C
T
T
F
F
T
T
F
F
T
T
T
F
T
T
T
F
D)
T
F
T
F
T
F
T
F
F
F
F
T
T
T
T
T
~
F
F
F
F
T
20. This statement is a tautology.
X
T
T
T
T
F
F
F
F
Y
T
T
F
F
T
T
F
F
Z
T
F
T
F
T
F
T
F
[(X
T
T
T
T
F
F
F
F
&
T
T
F
F
F
F
F
F
T
F
T
T
T
T
T
T
Y)
T
T
F
F
T
T
F
F
Z]
T
F
T
F
T
F
T
F
[(X
T
TT
T
TF
T
T
EXERCISES FOR SECTION 3.4
PART I: TAUTOLOGIES
(Note: You can find solutions to the odd-numbered problems in the authors solutions manual,
which you can find at the following web site: http:/blue.butle
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
B C.
This is an SL statement. It has the logical form of a conjunction; & is its
main connective. (The parentheses around B are OK (since B is a
statement lette
25.
N: There is a nuclear war; U: It will be started by the United States; R: It will be
started by Russia.
N (U R )
~U & ~R
~N
26.
G: The game will be won; S: Samson is allowed to play; T: Samson is
33.
R: I will allow you to read the comics; G: You give me the front page. (R G)
EXERCISES FOR S ECTION 2.4
PART I
2.
L: Luc will stay at the party; A: Andy will stay at the party. (L A) & ~(L & A)
3.
16.
Truth-functionally compound. The simple statements are The man walked up to
the stand and The man ordered an ice cream cone.
17.
Truth-functionally simple.
18.
Truth-functionally simple.
20.
Truth
SOLUTIONS TO SELECTED EXERCISES
EXERCISES FOR S ECTION 2.1
PART I
1.
Given the form p. Case (a): Let p be the statement Salt Lake City is in Utah.
Then p is true. Case (b): Let p be the statement Salt
Limits of sl
Objects and properties
Quantication
The universal quantier
But we also have a symbol we can for statements about
everything: . This symbol is called the universal quantier,
and when used
Limits of sl
Objects and properties
Quantication
Homework
Warm-up
Translate this argument into sl form and then determine whether
its valid:
Every place in Illinois gets cold in the winter. DeKalb is
Four Types of General L-Statements
A
All S are P.
All surgeons are doctors.
x(Sx
Dx)
E
No S are P.
No crabs are crows.
x(Cx
~Rx)
I
Some S are P.
Some apples are pippins.
x(Ax & Px)
O
Some S are not P.
50. This argument is valid.
A
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
B
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
C
T
T
T
T
F
F
F
F
T
T
T
T
F
F
F
F
T
T
T
58. M: My computer makes mistakes; C: My computer has been correctly programmed; P:
There is a power failure.
~(~C P) ~M
~P & M
~C
The following truth table shows that this argument is valid:
C
T
T
T
I. Pre-Test Extra Credit: Prove the following using ONLY the rules of PD. (5 points each; 25
points total)
a. Prove validity: cfw_(x)(Fx Gx), Fb Hb (y)(Fy Hy)
b. Prove validity: cfw_(x)(Fx), (y)Gy) (z
FORMAL LOGIC
SYMBOLIZATION WITH POLYADIC PREDICATES
Monadic Predicates
Hx = x is a house
Dx = x is a day
Px = x is a person
LESSON PLAN
PROFESSOR JULIE YOO
Polyadic Predicates Predicates
Lxy = x likes
FORMAL LOGIC
PL BASIC CONCEPTS
LESSON PLAN
PROFESSOR JULIE YOO
Predicate Logic (PL) v Sentential Logic (SL)
Inadequacy of SL: SL can only represent logical relations among whole sentences, not
logical
FORMAL LOGIC
PD INTRO AND ELIM RULES
Universal Elimination
Universal Elimination (E)
(x) P
P (a / x)
Existential Introduction
Existential Introduction (I)
P (a / x)
(x) P
Universal Introduction
Univer
lL Ml361:1" 'TION AND SD AND SD+ ' PROFESSOR JULIE YOO
Name: : ;Z2 Lid/cfw_l0 K?
I. PL Translations: (2 points each; 50 points total 2 points free)
Symbolization Key UD: Unrestricted Sx = x can swim
P
FORMAL LOGIC
SYNTAX OF PL
LESSON PLAN
PROFESSOR JULIE YOO
A Quantifier of PL
A quantifier of PL is an expression of PL of the form (x) the universal quantifier or (x)
the existential quantifier.
Atom
FORMAL LOGIC
SYMBOLIZATION WITH MONADIC PREDICATES
LESSON PLAN
PROFESSOR JULIE YOO
Basic Universal and Existential Statements A, E, I O
Subjects/Constants
(none)
Predicates
Sx = x is a swan
Wx = x is
FORMAL LOGIC
EXPLANATION OF PD RULES
LESSON PLAN
PROFESSOR JULIE YOO
FOUR NEW RULES OF PD
Inferences in PD Require Replacement of Variables with the RIGHT Constants
The derivation system, PD, adds fou
PHILOSOPHY 230
INTRODUCTION TO FORMAL LOGIC
PROFESSOR JULIE YOO
DEPARTMENT OF PHILOSOPHY
CALIFORNIA STATE UNIVERSITY AT NORTHRIDGE
Tu and Th 3:30 4:45
Juniper Hall 1206
Class (Ticket) No: 14556
email:
FORMAL LOGIC
PL SYMBOLIZATION AND SD AND SD+
EXAM #3
PROFESSOR JULIE YOO
Name: _
I. PL Translations: (2 points each; 50 points total 2 points free)
Symbolization Key
UD: Unrestricted
Px = x is a pengu
E
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
M
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
P
T
T
T
T
F
F
F
F
T
T
T
T
F
F
F
F
T
T
T
T
F
F
F
F
T
T
T
T
F
F
F
F
R
Limits of sl
Objects and properties
Quantication
Homework
Something
Now consider the following statement:
1. Something is hilarious.
Let H name the property of being hilarious. You might think we
shou
Limits of sl
Objects and properties
Quantication
Homework
Predicates as truth-functions
From objects to truth values
You can think of a predicate letter as determining a function from
objects to truth
1. Assume the opposite of the conclusion if the conclusion has a quantifier.
2. Double negation
3. Quantifier exchange
4. Existential Generalization (EG)
OR
Existential instantiation (EI)
5. Universal
Interpretations
Homework
Interpretations
Polyadic predicate letters
An interpretation assigns a two-place predicate letter a set of
ordered pairs; for example:
[L] = cfw_<Alex, Beth>, <Beth, Chris>, <
Interpretations
Homework
Interpretations
Review of sl interpretations
Just as in sl, a formula in q is neither true nor false without an
interpretation. We need to assign them meanings to get them to