Homework 1: Due Tuesday, March 12
Name:
Viviene
Huang
Instructions: You are permitted to discuss these questions with your classmates
and consult the Internet. But please keep in mind that the goal of this homework
is to prepare you for the midterm exam. Copying answers from your classmates’
homework is a very ine↵ective way of preparing for the exam. Also, please try to
write neatly. Good luck!
A. For each argument, indicate whether it is: formally valid, valid but not formally valid, or invalid. For each formally valid argument, provide the form of
the argument. For each argument that is valid but not formally valid, provide an
argument of the same form that is invalid. And for each invalid argument, provide
a counterexample that shows that the argument is invalid. (10 points)
1. If Je↵ slept through class yesterday, he’ll get an A on tomorrow’s test. Je↵
slept through class yesterday. Therefore, he’ll get an A on tomorrow’s test.
Circle one:
formally valid
A
>
If A then C
:
invalid
conditional
'If
C
valid but not formally valid
...
then'
2. Melissa went to Family Mart on Monday or Tuesday. She went on Monday.
So she didn’t go on Tuesday.
Circle one:
A
or
formally valid
B
V
not-B
:
invalid
disjunction
Either
A
valid but not formally valid
...
or
...
3. Chelsea is brown. Chelsea is a puppy. Therefore, Chelsea is a brown dog.
Circle one:
Chelsea
Chelsea
Chelsea
formally valid
is
is
is
valid but not formally valid
invalid
brown
a
puppy
a
brown
doll
in
puppy shape.
2
4. If it rains tomorrow, the party will be cancelled. It won’t rain tomorrow. So,
the party won’t be cancelled.
Circle one:
formally valid
If it
tomorrow
rains
It
won't
be
cancelled
rain
,
valid but not formally valid
the
party
tomorrow
will be
but the
because the
invalid
.
cancelled
party
still
supermarket
is
closed
5. Samantha is an alligator. Therefore, Samantha is not a crocodile.
Circle one:
formally valid
valid but not formally valid
invalid
B. Using the symbolization key given, symbolize each English sentence in TFL. (5
points)
A: Steve Rogers is old.
B: Natasha Romano↵ is funny.
C: Tony Stark is rich.
D: Peter Parker is young.
E: Sam Wilson has a beard.
F : Steve Rogers has a beard.
1. Either Sam Wilson or Steve Rogers has a beard, but not both.
(EVF)
2. Steve Rogers has a beard unless Sam Wilson does.
LEVF)
3. Peter Parker is young only if Steve Rogers is old.
(D > A)
-
4. If Natasha Romano↵ isn’t funny, then Tony Stark isn’t rich.
-C)
5. Natasha Romano↵ is funny if and only if Tony Stark is rich.
(
-
B
(B
+
>
-
C)
.
3
C. Write complete truth tables for the following sentences and mark the column
that represents the possible truth values for the whole sentence. (33 points)
1. (A ! B) $ (B ! A)
A
T
I
F
B
+
T
T
T
F
E
F
E
# +
+
T
B
>
A
T
T
-
-
E
T
F
F
T
F
2. (C _ D) ^ ¬(C ^ D)
C
1
VD
C1D
-
EY I IEE
T
T
3. ¬(E ^ F ) $ (¬E _ ¬F )
-
F
E
+
7 T
FI
F
F
1
T
T
T
i
Es
T
-
F
E
↑
EEFT
7
E
T
Y
V
F
-
F
FT
TTF
F
T
F
F
T
+
T
F
4
4. P ! (Q ! R)
+
Q
+
T
T
T
T
↑
T
F
+
T
P
T
R
T
i
F
F
F
T
T
T
F
F
5. (L ^ M ) ! N
M
L
1
T
I
T
T
T
>
-
N
T
z
+
T
F
F
T
F
F
T
F