Introductory Logic 
Test #2

March 20, 2006

Name: ________________________ 
R. Hammack

Score: _________

(a)  Your test grade will be dropped only if it is your lowest grade or you have an excused absence. 
Y ⊃ (L ∨ E)  Y = "Your test grade will be dropped." L = "It is your lowest grade." E = "You have an excused absence." 
(b)  If it does not rain soon, then the risk of forest fires will be great and cuation will be necessary. 
~R ⊃ (F • C)  R = "It rains soon." F = "The risk of forest fires will be great." C = "Cuation will be necessary." 
(c)  Oregon does not have a sales tax, but Virginia does. 
~O • V  O = "Oregon has a sales tax." V = "Virginia has a sales tax." 
(d)  If affirmative action programs are dropped, then if new programs are not created, then minority applicants will suffer. 
A ⊃ (~N ⊃ M)  A = "Affirmative action programs are dropped." N = "New programs are created." M = "Minority applicants will suffer." 
(e)  Yosemite and Kings Canyon restrict vehicle traffic unless Bryce and Zion do not. 
~(~B • ~Z) ⊃ (Y • K) OR (B ∨ Z) ⊃ (Y • K) OR (Y • K) ∨ (~B • ~Z) 
Y = "Yosemite restricts vehicle traffic" K = "Kings Canyonrestricts vehicle traffic" B = "Bryce restricts vehicle traffic" Z = "Zion restricts vehicle traffic" 
(a) 

(b) 

3. (24 points) Determine if the following pairs of statements are logically
equivalent, contradictory, consistent, or inconsistent.
(a) 

(b) 

(c) 

(a) 
P

⊃

(

R

≡

A

)

/

A

⊃

(

W

•

~

R

)

/

R

≡

(

W

∨

K

)

/

P

•

U

/

U

⊃

K

T

T

T

T

T

T

T


?

F

F

T

T

T

?

T

T

T

T

T

T

T

T


(b) 
M

∨

B

/

~

B

/

M

•

A

/

B

⊃

M

/

A

∨

B

T

T

F

T

F

T

T

T

F

T

T

T

T

F


(a) 

M

⊃

(

C

∨

D

)

/

~

X

∨

M

/

(

D

∨

C

)

⊃

X

//

M

≡

X

T

T


F

F

F

T

F

T

T

F

F

F

T

F

T

F

F


F

T

F

T

T

F

T

T

F

F

T

There are two ways for the conclusion to be false, and a line is filled in
for each way. Notice that there is a contradiction on both lines, so the argument
is VALID
(b) 

M

⊃

(

L

⊃

K

)

/

P

⊃

M

/

~

S

/

S

∨

L

//

K

⊃

P

?

T

T

T

T

F

T

?

T

F

F

T

T

T

F

F


Notice that when the table is filled out, the value of M cannot be determined. However, if you set M=T (or F), all the premises are true and the conclusion is false. Therefore the argument is INVALID.