PHL111 Valid Reasoning, Past Assignments
Reading: Read chapter 1 of CIL.
Practice: Hand in at the beginning of class your answers
to problems 1-5 at the end of chapter 1. Each of these problems
asks you to come up with 5 examples; to make the homework
shorter, for each problem just come up with 2 examples.
Handwritten is acceptable (for many of our later homeworks there
are special symbols or tables and it is too much work to try to
Reading: Read chapter 2 of the book.
Practice: Complete problems 5 and 6 at the end of chapter 2.
Reading: Read chapter 3 of the book.
an alternative view of arguments (especially in the minute starting
around 1:40 and following); one closer to the colloquial use of the
word "argument"--but different than our technical use of the word.
Read: chapter 4 of CIL.
Homework: do problems 1a, 1b, 2a, 2b, and 3 of chapter 3.
NOTE: I have an unexpected emergency, and must cancel
my offices hours this afternoon. Write me and we'll find time
for you Monday if you need to see me.
Alternative homework: Some people found the last homework
confusing and did not manage to complete it correctly. If you want
to try a redo, or a first/late do, you can instead do the following:
chapter 3 problems problems 1c, 1d, 2c, 2d, and 3.
Please note: I've been informed that the book does not
load correctly on a phone! Sorry. Be sure you read it on a computer
screen in order to see the truth tables correctly!
Practice: Do problems 1 and 4 of chapter 4. This is nine
proofs, but they are short, and a good block of practice will help
you become familiar and comfortable with direct derivations.
Reading: Read chapter 5 of the book.
Practice: Of chapter 5, do problems 2a, 2b, 2d, 2e; and 3a,
3b, 3c, 3d.
NOTE: "Direct derivation" is another way of
saying "direct proof." So if I ask for a direct derivation I am
asking for a direct proof (and not a truth table). Thanks!
Our slides from last class
as a pdf.
is a printable version of chapter 10. Print it and keep it with
I apologize, but I have a conflict with my office hours on this
day and will not be able to hold my office hours. Email me and
we can meet another time if you need to talk with me.
Read: chapter 6 of A Concise Introduction to Logic.
There is a philosophy talk on
Mind, Metaphysics, and the Future, by
Pete Mandik. It's in our classroom, from 4:00 to 5:00 pm. This
will be a fun talk and I will give extracredit to encourage you to
come (sign up in the back of the room to get the extra credit, which
will be worth the equivalent of a homework).
Practice: Of chapter 5, do problem 7; of chapter 6 do problem 1.
NOTE: my office hours must start at 2:00 today, but they can run
as late as you would like!
I will have office hours from 1 to 3 pm. Please note that I cannot
have office hours on Friday, and Wednesday is our holiday, so this
would be a good time to see me this week if you need me. Try out
the next homework now so you know if you need some help.
Practice: due at the beginning of class. From chapter
6 do problems 2b, 2d, and 4.
I apologize but I have a conflict this afternoon and cannot have my
office hours at 1:30. Please contact me should you need to see me.
Some of you asked me for practice problems. Here are a few.
I will post answers later. These include "or", but that's good
because we haven't practiced that yet.
Here are some practice translations. Make a key and translate the
are my answers, without the proofs yet.
- Neither Fry nor Bender eat Bachelor Chow.
- If either Fry or Bender eat Bachelor Chow, then Fry will
- Bender eats bachelor chow only if Fry drinks slurm.
- Bender eats bachelor chow if Fry drinks slurm.
- Either Bender doesn't eat Bachelor Chow or Fry does.
For these next two problems, create a key, translate the passage,
and prove the argument is valid using a proof.
- Either the Professor Plum or Miss Scarlet killed Colonel
Mustard. If Professor Plum killed Colonel Mustard, then
Professor Plum was in the kitchen. If Miss Scarlet killed
Colonel Mustard, then she was in the drawing room. If Miss
Scarlet was in the drawing room, then she was wearing boots.
But Miss Scarlet was not wearing boots. So, Professor Plum
killed the Colonel.
- Either Mrs. White or Mrs. Peacock stole the diamonds.
If Mrs. Peacock stole the diamonds, then she was in the
billiards room. But if Mrs. Peacock was in the library,
then she was not in the billiards room. Therefore, if
Mrs. Peacock was in the library, Mrs. White stole the diamond.
Here is a proof for 6, and
Here is a proof for 7.
In addition to the practice problems of 17 October, here are some
more. Try to prove the following theorems.
a proof for 1, and Here is
a proof for 2, and Here is
a proof for 3.
- (((P ^ Q) → R) → (P → (Q → R)))
- ((P → (Q → R)) → (Q → (P → R)))
- (((P → (Q → R)) ^ Q) → (P → R))
Extra credit. I'll give extra points to anyone who can do the
following. You can work in teams; just let me know everyone in
your team. Keep it to fewer than 6 people per team, please. Hand
it in on Friday at the beginning of class.
Translate the following passage into propositional logic. Prove the
argument is valid using a direct proof. (This is review of older
stuff, since it does not require a conditional derivation.)
If Miss Scarlet killed the colonel, then she was in the billiards
room. Professor Plum has chalk on his hands. Miss Scarlet has
chalk on her hands, and she shook hands with Professor Plum. If
Miss Scarlet has chalk on her hands, then if she shook hands with
Professor Plum, then she was not in the billiards room. If
Professor Plum did not kill the colonel, then Miss Scarlet killed
the colonel. We deduce that Professor Plum killed the Colonel.
Test 1 in class. Specific topics include: meaning of each of the
connectives (that is, the defining truth table for the connective);
direct and conditional derivations; translations; meaning of valid,
sound, tautology, theorem, contingent sentence, and contradictory
sentence; using truth tables to determine the meanning of a complex
sentence; using truth tables to perform a semantic check of an
Read chapter 8.
In case anyone is interested, the College of Liberal Arts and
Sciences is having its Brown Bag lunch conversation on "Election
2016: Beyond the Soundbite," a discussion on what has been left out
of the national conversations during this election cycle. The
topics are: "A Vision of Other Economies" (me), "The Aftermath of
Mass Shootings: The Gun Debate and National Crime Statistics"
(Jacklyn Schildkraut), and "A Defense of Intellectualism and
Science" (Shashi Kanbur). This is from 12:30 to 2 p.m. in the
Speakers Corner of Penfield Library. You can bring food and eat it
Practice: from chapter 7 do problems 1, 2, and 3a, 3b, 3c, 3d, 3e.
Practice: From chapter 8, do problems 1a, 1b, 1c, 1d, 2c, and
2d. Those from chapter 8 will require one or more indirect
derivations. (Please note there is an error in the book; chapter 8,
2b is not a theorem! I'll fix that asap.)
More demands of you! You should watch these
five videos by Dr. Chew, now that you've taken your test and had
time to reflect on logic and your work. These will only take 30
minutes of your time and they are fantastic advice.
Read: chapter 9 of the book.
Practice: from chapter 9 do problem 1.
Read: chapter 11.
Read: chapter 12 of CIL.
Practice: do problems 1, 2, and 3 of chapter 11.
Quiz 2: all of the propositional logic (new things are
indirect proofs and biconditionals), plus translating with
names and predicates (but not with quantifiers yet).
Read: chapter 12 of CIL.
Read: chapter 13 of CIL.
Read: chapter 14 of CIL.
You should print, and keep with you, chapter 10 (a
complete introduction to the propositional logic and chapter 16 (a
complete introduction to the First Order Logic. These links
are to pdfs of my own version of the book; they are not as nicely
formatted but they are printable.
Practice: from chapter 12, do problem 2.
Practice: from chapter 13, do problem 1.
Practice: from chapter 13, do problems 2 and 3.
Problem 2c is the hardest we've done all semester! But, as a
hint, look at the second example in section 9.6 of the book.
The structure of part of that proof is similar to what you will
Extra: I promised some extra practice for
translations using quantifiers. Here's something you can do this
week for extra credit if you like.
Domain of discourse: people
Fx: x likes strawberry poptarts.
Gx: x is a barbarian.
Hx: x likes schmors poptarts.
Ix: x is civilized.
Jx: x is a gourmand.
- Some like strawberry poptarts.
- All who like strawberry poptarts are civilized.
- All who are not civilized do not like strawberry poptarts.
- Some don't like strawberry poptarts.
- Tony likes schmors poptarts but Sam does not.
- No one who likes strawberry poptarts likes schmors poptarts.
- Anyone who likes schmors poptarts is a barbarian.
- No one likes schmors poptarts.
- Some who like schmors poptarts are not gourmands.
- Some who like strawberry poptarts are gourmands.
- Sam is civilized if and only if Tony isn't.
- No one is a civilized barbarian.
Some extra office hours: I'll be available from 2-3 pm, and perhaps
longer if required.
Practice: from chapter 14, do problem 1.
Some hints: variables are just placeholders! Don't get
scared if a formula uses a different variable. Remember how
in math you don't care if we use x or y. Also: the last three
problems are hard! Look at my proof at the end of the chapter
for some ideas. But most of all, if you can't do them, that's
OK. Think of them as extra credit!