THE LOGIC BOOK, 4TH EDITION: CHAPTER FIVE: SL DERIVATIONS Whales breathe by lungs and whales are warm-blooded. If whales breathe by lungs, then whales are not fish. Whales are warm-blooded and whales are not fish. 1. Whales breathe by lungs and whales are
WHAT IS ON THE EXAM? Anything we have studied can be on the exam. Derivations: approximately 35% of the exam. Focus on questions from the second half of the course. PANIC ATTACKS A VICIOUS CIRCLE When you don't see the solution, you panic. When you panic,
PHL 245: Second Practice Test Answers
A1: a advertises. D1: a has diamonds on it. G1: a is a restaurant M2: a is getting married to b. a0: Tiffany's d1: the fianc of a 1. B1: E1: H1: N2: a is a business a is an engagement ring. a stays in business. a is m
UNIT 1
REASON AND ARGUMENT
1.1 WHAT IS MODERN SYMBOLIC LOGIC?
Logic.
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
alread
UNIVERSITY OF TORONTO
Faculty of Arts and Science
EXAMINATION APRIL 2013
PHL 245 HIS
L0101 - Niko Scharer
Duration - 3 hours
Examination Aid: Sheet with rules (provided)
Last Name
First Name
Student Number
Answer all questions on the exam paper.
University of Toronto PHL 245 Modern Symbolic Logic Staple this page with your answers. St. # First name:
Test 2 Instructor Sorin Bangu
August 4th, 2005 - LM 159 45 minutes (8:10 8:55 PM) Worth 30% of the final grade. Answer all questions. Rules provided.
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
Modern Symbolic Logic
Week II: Sentential Logic - Getting Started
Kevin Kuhl
Department of Philosophy
University of Toronto
Announcements
Assignment 1: Rescheduled - details to follow on
Blackboard (still setting up online database for Logic2010)
Logic2
CSC384. Propositional Logic
February 16, 2016
1. Using Truth Tables, are the following statements equivalent?
(a) > and
2. Using Truth Table, is the following logical expression correct?
(a) (x S1 ) (x S2 ) > S1 S2
(b) (X (Y X) > Y
3. If a triangle is eq
CSC363 Tutorial 5
Reductions
Tutor: Assimakis Kattis
Scribe: Robert Robere
February 9, 2016
In this tutorial we classified the following two languages with respect to the computability
classes D, SD, coSD:
EMPTY = cfw_hM i | M is a TM that does not accept
1.
Consider the following argument:
If an argument is valid, then it has a true conclusion.
Arguments with a contradiction in the premises are valid.
Therefore, arguments with a contradiction in the premises have a true conclusion.
a)
Is the argument vali
1)
Not all soccer players try hard even though nobody likes losing. (3)
A: a is a person. C: a is a soccer player. D: a tries hard. F: a likes losing.
~x(CxDx) ~x(AxFx)
x(Cx~Dx)
x(Ax~Fx)
2)
Amongst amusement parks and zoos, those that have lions are popul
Derivation Types:
Direct Derivation (DD or dd)
Conditional Derivation (CD or cd)
Indirect Derivation (ID or id)
10 Basic Rules for Sentential Logic:
Modus Ponens (MP or mp)
( )
Double Negation (DN or dn)
~
~
Simplification (S/SL/SR or s/sl/sr)
Addition
For questions 1-3, symbolize the English sentence using the abbreviation scheme provided for each
question.
1.
Unless drinking coffee is necessary for Tom to be alert, he will pass the test even though he
neither studied nor slept. (4)
P: Tom drinks coffe
For questions 1-3, symbolize the English sentence using the abbreviation scheme provided for each
question.
1)
Assuming that Jon is not both late and smelly, he will be in trouble only if Bill is neither
angry nor busy. (4)
P: Jon is late. Q: Jon is smell
1)
Only nurses have a thankless job. (3)
A1: a is a nurse. B1: a is thankless. C1: a is a job. B2: a has b.
x(y(CyByB(xy)Ax) and all exportation forms work too.
x(~Ax~y(CyByB(xy)
x(~Axy(CyBy~B(xy)
If they put: xy(CyByB(xy)Ax), this is wrong! That y needs
1)
A sufficient condition for teachers and students being friendly is that they are neither angry
nor tired. (3)
A1: a is a teacher. B1: a is a student. D1: a is angry. F1: a is friendly. G1: a is tired.
x(AxBx(~(DxGx)Fx)
x(AxBx)~(DxGx)Fx)
~(DxGx) can be
1)
ww
w.
ox
di
a
Put the following argument into standard form. (3)
Classical music is boring and outdated. I definitely think that because of this, many
kids are not enrolling into music classes. It really does seem that we should abolish
classical music
S 2.9 E1a
U: Determinism is true. V: I am free.
Determinism is true but I am free.
Basic Page 1
S 2.9 E1c
U: Determinism is true.
V: I am free.
Determinism is false, however I am not free.
Basic Page 2
S 2.9 E1e
P: I exist.
I exist if I think.
Basic Page
Old Test 2014S 2
September 20, 2016
11:45 AM
Construct a full truth-table for the following set of sentences.
What property does the set have?
cfw_R~PQ, ~(PR)Q
P
Q
R
R
~
P
Q
~
(P
R)
Q
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
F
T
F
T
Modern Symbolic Logic Week 2
Kevin Kuhl
Department of Philosophy
University of Toronto
Outline
1
Symbolizations in Sentential Logic
Complex Sentences
Consider:
Either Kevin is 6ft tall or Kevin is not 6ft tall
How does the Either.or. contribute to the mea
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
PHLB50 Unit 3 Part 2
SL Derivations Contd
0. Re-cap
Derivations are one of the basic techniques we will use for testing validity.
A derivation is a special way of representing an argument we start by
specifying our premises and which conclusion we want to
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
Sentential Derivation Problems
BASIC DERIVATION PROBLEMS NO SUBDERIVATIONS
These questions just use MP, MT, DN and R. They require no subderivations.
They are meant to help those who want more exercises to get used to the basic rules and derivation types.
PHL245: Truth Tables Handout
Recall our definition of validity:
an argument is valid if and only if the conclusion is true if the premises are true
We used derivations as one test for validity. By showing
Modern Symbolic Logic Week 3: SL and
Symbolization Contd
Kevin Kuhl
Department of Philosophy
University of Toronto
Announcements
Assignment 1: Rescheduled! Questions will be released
and Logic2010 link will be posted today, still waiting on
database to b
Syllabus
PHL 245 H1S
Daniel Bader
MW6-9
Textbook:
The course text is An Introduction to Symbolic Logic by Terence Parsons, and is
available at no charge online at: HYPERLINK "http:/www.humnet.ucla.edu/humnet/
phil/faculty/tparsons/Phil%2031/" http:/www.hu
1.
Given that the Raptors will make the playoffs unless disaster strikes, only if Albert gets
cable will he be not both sad and lonely. (4)
P: The Raptors will make the playoffs. Q: Albert gets cable. R: Albert will be sad.
S: Albert will be lonely. T: Di
1.
People never tell the truth. (3)
F1: a is a person. H1: a is a time. G2: a tells the truth at b.
x(Fx(y(Hy~G(xy)
x(Fx~y(HyG(xy)
2.
Even though Selina looks older than her brother, she sometimes gets carded at the
LCBO. (4)
a0: Selina. a1: The brother o
For questions 1-3, symbolize the English sentence using the abbreviation scheme provided for each
question.
1)
Although not all of Adam, Bob, and Ethel eat meat, none of them will have a stomach ache
when Jamie cooks. (4)
P: Adam eats meat.
Q: Bob eats me
1)
John Tory is the mayor of Toronto, but not everyone voted for him. (3)
a0: John Tory. b0: Toronto. b1: The mayor of a. D1: a is a person. G2: a voted for b.
a=b(b) ~x(DxG(xa)
x(Dx~G(xa)
NOTE: in the G(xa) you could also write G(xb(b)
2)
A bar that does