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