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Philosophy 103: Introduction to Logic
Test: Symbolic Logic

Topic: Theory Construction in Economics

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SYMBOLIC LOGIC  TEST PART II: 
ARGUMENT FORMS

RETURN TO TEST ON SYMBOLIC LOGIC INDEX PAGE

Part II:  Argument Forms.  Professor Usurer claims:

  1. His fourth law can be deduced from the higher-level law (1).
  2. His fifth law follows from higher-level law (2), and
  3. His sixth law can be deduced from higher level law (4).

Evaluate his claims.

A.  His fourth law can be deduced from the higher-level law 1--Answer

Higher Level Law (1):

 

Form
(P  and  Q)  implies  (R   and  T)   premiss

(p  and   q)  implies  (r   and  t)
Prof. Userer's Fourth Law:

Q  implies  R

 

  ergo  q  implies  r


premiss conclusion

 

p

q

r

t

p  and   q

r   and  t

(p and q)  implies  
(r and  t)

q  implies  r

 

1

T

T

T

T

 

T

 

 

T

 

 

T

 

T

 

2

T

T

T

F

 

T

 

 

F

 

 

F

 

T

 

3

T

T

F

T

 

T

 

 

F

 

 

F

 

F

 

4

T

T

F

F

 

T

 

 

F

 

 

F

 

F

 

5

T

F

T

T

 

F

 

 

T

 

 

T

 

T

 

6

T

F

T

F

 

F

 

 

F

 

 

T

 

T

 

7

T

F

F

T

 

F

 

 

F

 

 

T

 

T

 

8

T

F

F

F

 

F

 

 

F

 

 

T

 

T

 

9

F

T

T

T

 

F

 

 

T

 

 

T

 

T

 

10

F

T

T

F

 

F

 

 

F

 

 

T

 

T

 

11

F

T

F

T

 

F

 

 

F

 

 

T

 

F

 invalid

12

F

T

F

F

 

F

 

 

F

 

 

T

 

F

  invalid

13

F

F

T

T

 

F

 

 

T

 

 

T

 

T

 

14

F

F

T

F

 

F

 

 

F

 

 

T

 

T

 

15

F

F

F

T

 

F

 

 

F

 

 

T

 

T

 

16

F

F

F

F

 

F

 

 

F

 

 

T

 

T

 

Prof. Userer's claim must be rejected.

B.  His fifth law follows from higher-level law (2)--Answer.

Argument

Form of Argument
(R  and  T)   implies  V  premiss

T    V  conclusion

(r  and  t)   implies  v  

    t     v

premiss  conclusion
r t v r  and  t (r  and  t)  implies  v   t   implies  v
1 T T T T T T
2 T T F   T     F       F    
3 T F T F T T
4 T F F F T T
5 F T T F T T
6 F T F   F     T       F invalid
7 F F T F T T
8 F F F F T T

Prof. Userer's claim must be rejected

C.  His sixth law can be deduced from higher level law (4).

Argument

Form of Argument
Higher Level Law (4):
V  implies  (U  or  T)  premiss

Userer's Sixth Law:
V  implies  U  conclusion

v  implies  (u  or  t) 

    v  implies  u
premiss  conclusion
t u v u  or  t v  implies  (u  or  t)  v  implies  u  
1 T T T T T T  
2 T T F   T     T       T      
3 T F T T T F invalid
4 T F F T T T  
5 F T T T T T  
6 F T F   T     T       T  
7 F F T F F F  
8 F F F F T T  

Prof. Userer's claim must be rejected

CONTINUE TO PART III: STATEMENT FORMS ANSWERS

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