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 makeup test only if you request it. 
M = "I will give you a makeup 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, selfcontradictory, 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.