Unit 3 Part 2: Derivation Exercises
Derivations with AND, OR and BICONDITIONAL
NOTE: there are 3 sections. Make sure you do a good number from each section. (In
each section, the first ones tend to be easier than the later ones.)
SECTION 1: Construct deri
Derivations Exercises 1: For Unit 3 Part 1
Derivations with NEGATION and CONDITIONAL
Construct derivations to validate each of the following arguments.
For the first set, use Direct Derivation only. Do not use ID or CD.
R S . S T. T
1.
R.
2.
T W. W X. ~X.
DERIVATIONS: NATURAL DEDUCTION
Part 1
3.2 E1
Which inference rule justifies the following arguments? (mp, mt, dn or none)
a)
~R P
~R
P
b)
P ~Q
Q
~P
c)
NONE!
DN cannot be
used on a
sentential part
MP
e)
~S T
ST
~(~P Q)
PQ
f)
P (P ~P)
P
P ~P
NONE!
First y
Derivations Exercises Unit 3 Part 1
Derivations with NEGATION and CONDITIONAL
SELECTED ANSWERS QUESTIONS 20-70
Answers only for selected derivations.
In the annotations: conc= conclusion, ant= antecedent, cons=consequent, cond=conditional
Use any derivati
UNIT 5 Part 1
SYMBOLIZATION: PREDICATES AND QUANTIFIERS
5.1: THE LOGIC OF SUB-SENTENTIAL RELATIONS
Consider this argument:
All humans are mortal.
Socrates is human.
_
Socrates is mortal.
It is clearly a valid argument, but if we try to symbolize it using
Unit 3 Part 2: Derivations Exercises
Derivations with AND, OR and BICONDITIONAL
.
SECTION 1: use only MP, MT, R, DN, ADD, S, ADJ, MTP, BC and CB
1.
(P Q) (R S). (P S) Q
1 Show (P S) Q
2
PQ
3
RS
4
P
5
Q
6
S
7
PS
8
( P S) Q
9
2.
must adjoin P S first
P Q. ~
DERIVATIONS WITH AND, OR AND BICONDITIONAL
NATURAL DEDUCTION
Part 2
3.11 Derivations with AND, OR and BICONDITIONAL
So far weve learned how to derive any sentence from any set of sentences that entails it, provided that
the sentences are symbolized using
UNIVERSITY OF TORONTO
Faculty of Arts and Science
DECEMBER 2015 EXAMINATIONS
PHL245H1F
Alex Koo
Duration - 3 hours
Examination Aid: Sheet with rules (provided)
Last Name: _
First Name: _
Student Number: _
Answer ALL questions on the exam paper.
Use examin
UNIVERSITY OF TORONTO
Faculty of Arts and Science
AUGUST 2014 EXAMINATIONS
PHL245H1Y
Alex Koo
Duration - 3 hours
Examination Aid: Sheet with rules (provided)
Last Name: _
First Name: _
Student Number: _
Answer ALL questions on the exam paper.
Use examinat
Derivations Exercises 1
Derivations with NEGATION and CONDITIONAL
ANSWERS QUESTIONS 1-19
I have included all the answers for the first two sections. After that, there will be answers only for
selected derivations.
For the first set, use Direct Derivation
UNIT 3: DERIVATIONS FOR SENTENTIAL LOGIC
NATURAL DEDUCTION
Part 1
3.1 What is a derivation?
A derivation is a proof or demonstration that shows how a sentence or sentences can be derived
(obtained by making valid inferences) from a set of sentences. A der
UNIT 4
SEMANTICS: FUN WITH TRUTH-TABLES
4.3 EG1 ~R S
R
T
T
F
F
A contingent sentence.
S
T
F
T
F
~
F
F
T
T
R
T
T
F
F
T
F
T
T
S
T
F
T
F
S
T
F
T
F
~
F
F
F
T
(R
T
T
F
F
T
T
T
F
S)
T
F
T
F
~(R S)
R
T
T
F
F
A contingent sentence.
4.3 EG2
Lets do a truth-table f
Symbolizations with multi-place predicates (Unit 5: Sections 5.6-5.9)
Symbolize each of the following sentences using the abbreviation scheme provided
A1: a is an animal.
D1: a is a dog.
a: Astro
B1: a is a mouse.
F2: a is afraid of b.
b: Bandit
C1: a is
Symbolization Exercises
Symbolizations with one-place predicates (Unit 5 Part 1: Sections 5.1-5.6)
Symbolize each of the following sentences using the abbreviation scheme provided:
A1: a is an athlete.
B1: a is beautiful.
C1: a works out.
F1: a is famous.
Symbolization Exercises
Symbolizations with one-place predicates (Unit 5 Part 1: Sections 5.1-5.6)
Symbolize each of the following sentences using the abbreviation scheme provided:
A1: a is an athlete.
F1: a is famous.
K1: a competes in the Olympics.
B1:
Day 1
2011 1 10
9:38
Modern symbolic logic is a study of deductive reasoning
o
Valid deductive argument that has true premises yields true conclusions
o
Logic is to understand critical analysis of what is true and what is false
By using symbols, confusi
UNIT 1
REASON AND ARGUMENT
1.1 WHAT IS MODERN SYMBOLIC LOGIC?
L ogic.
The Study & Evaluation of Reasoning & Argument
An argument probably seems logical if it look likes the conclusion
must be true, based on what you are told is the case and what you
alrea
UNIT 1: REASON AND ARGUMENT
Answers to exercises
1.4 E 1
Some students will undoubtedly pass this course. Hence it is clear that some students in this
class will do the exercises, since nobody passes who doesnt do at least some of the exercises.
Some stud
UNIT 2
SENTENTIAL LOGIC: SYMBOLIZATION
2.1 WHAT IS SENTENTIAL LOGIC?
Sentential Logic (SL): A branch of logic in which sentences or propositions are used as the basic
units. It is also called Propositional Logic or Propositional Calculus.
We will use a sy
UNIT 2
SENTENTIAL LOGIC: SYMBOLIZATION
Answers to Exercises
UNDERSTANDING THE MATERIAL CONDITIONAL
A LITTLE LOGIC PUZZLE: Discussion & Answers
2.4 E1
Every card has a number on one side and a letter on the other. Suppose there is a rule:
If one side of a
UNIT 2: SYMBOLIZATION EXERCISES 2
Symbolizing with Conjunction, Disjunction and Biconditional
Symbolize each of the following sentences using the abbreviation scheme provided:
P:
Q:
R:
S:
Polly will pass the course.
Quincy will pass the course.
Ryan will
UNIT 2: SYMBOLIZATION 2
(WITH CONJUNCTION, DISJUNCTION AND BICONDITIONAL)
Answers to Exercises
P:
Q:
R:
S:
Polly will pass the course.
Quincy will pass the course.
Ryan will pass the course.
Polly will study.
T:
U:
W:
V:
Quincy will take the exam.
Quincy
UNIT 2: SYMBOLIZATION EXERCISES 1
Negation and Conditional
Symbolize each of the following sentences using the abbreviation scheme provided:
P: The Toronto Maple Leafs win.
Q: The Washington Capitals win.
R: The Vancouver Canucks win.
S: The Edmonton Oile
UNIT 2: SYMBOLIZATION EXERCISES 1 ANSWERS
Negation and Conditional
Symbolize each of the following sentences using the abbreviation scheme provided:
P: The Toronto Maple Leafs win.
Q: The Washington Capitals win.
R: The Vancouver Canucks win.
S: The Edmon