Introductory Logic |
Test #2
|
January 13, 2006
|
Name:_________________________ |
R. Hammack
|
Score: _________
|
(a) | A day is a test day if and only if the day is a Friday and the month is January. |
(b) | I will give you a make-up test only if you request it. |
M = "I will give you a make-up test"
Y = "you request it"
M ⊃ Y
(c) | If the Internet use continues to grow, then more people will become cyberaddicts, and normal human relations will deteriorate. |
(d) | We will have a picnic unless it rains. |
(e) |
If you hold down the shift key and press the delete button, then your computer will explode, and you'll have to buy a new one and rewrite all your files. |
(H • P) ⊃ (E • B • R)
2. (20 points) Write out the truth tables for the following propositions.
For each proposition, say if it is tautologous, self-contradictory, or contingent.
(a) |
|
TAUTOLOGOUS |
(b) |
|
CONTINGENT |
3. (20 points) Determine if the following pairs of statements are logically
equivalent, contradictory, consistent, or inconsistent.
(a) |
|
CONTRADICTORY and INCONSISTENT |
(b) |
|
LOGICALLY EQUIVALENT and CONSISTENT |
4. (20 points) Use indirect truth tables to decide if the following sets
of statements are consistent or inconsistent.
(a) |
K
|
≡
|
(
|
A
|
•
|
~
|
P
|
) |
/
|
A
|
⊃
|
(
|
P
|
•
|
~
|
S
|
) |
/
|
S
|
⊃
|
~
|
K |
/
|
A
|
•
|
~
|
K |
F
|
T
|
T
|
F
|
F
|
T
|
T
|
T
|
T
|
T
|
T
|
F
|
F
|
T
|
T
|
F |
T
|
T
|
T
|
F |
There is no contradiction, so the statents are CONSISTENT.
(b) |
(
|
Q
|
∨
|
K | ) |
⊃
|
C |
/
|
(
|
C
|
•
|
P | ) |
⊃
|
(
|
N
|
∨
|
L | ) |
/
|
C
|
⊃
|
(
|
P
|
•
|
~
|
L | ) |
/
|
Q
|
•
|
~
|
N |
T
|
T
|
? |
T
|
T |
T
|
T
|
T |
T
|
F
|
F
|
F |
T
|
T
|
T
|
T
|
T
|
F |
T
|
T
|
T
|
F |
A contradiction is highlighted, so the statents are INCONSISTENT.
(Note that the value of K cannot be determined, but this does not matter,
because, since Q=T, the statement Q∨K is true no matter what the value of
K is.)
5. (20 points) Use any technique from Chapter 6 to decide if the following
arguments are valid or invalid.
(a) | Elvis was a space alien or he was not a hound dog. If Elvis was a space alien, then he's still alive. Thus, if Elvis was a hound dog, then he's still alive. |
S = "Elvis was a space alien"
H = "Elvis was a hound dog"
A = "Elvis is still alive"
Writing the argument in symbolic form, and filliing out an indirect truth table
with true premises and false conclusion, we get:
S
|
∨
|
~
|
H |
/
|
S
|
⊃
|
A |
//
|
H
|
⊃
|
A | ||||||||||||||||||||||
F
|
T
|
F
|
T |
F
|
T
|
F |
T
|
F
|
F |
(b) |
|
Filling out an indirect truth table, with true premises and false conclusion, we get:
J |
⊃
|
(
|
~
|
L
|
⊃
|
~
|
K | ) |
/
|
K
|
⊃
|
(
|
~
|
L
|
⊃
|
M | ) |
/
|
(
|
L
|
∨
|
M | ) |
⊃
|
N |
//
|
J
|
⊃
|
N | |
T |
T
|
T
|
F
|
T
|
T
|
F |
F
|
T
|
T
|
F
|
F
|
F |
F
|
F
|
F |
T
|
F |
T
|
F
|
F |
There is no contradiction, so the argument is INVALID.