Analyzing Arguments

Objectives:
  • Determine the validity of an argument using a truth table.
  • State the conditions under which an argument is invalid.



Vocabulary:
  • valid argument
  • hypothesis
  • conclusion


Possible Classroom Examples:

p: It is Tuesday.
q: The tour group is in Belgium.

1. If it is Tuesday, then the tour group is in Belgium.
2. The tour group is not in Belgium.

Therefore, it is not Tuesday.

p
q
H1:
H2:
H1 and H2
C:
H1 and H2 implies C
T
T





T
F





F
T





F
F






If you are not in a hurry, you eat at Lulu’s Diner.  If you are in a hurry, you do not eat good food.  You eat at Lulu’s.  Therefore, you eat good food.
p:
q:
r:


Hypothesis 1:
Hypothesis 2:
Hypothesis 3:

Conclusion:

p
q
r

H1:

H2:
H1 and H2
H3: H1 and H2 and H3
C:
H1 and H2 and H3 implies C
T
T
T
  
  

  






T
T
F










T
F
T










T
F
F










F
T
T










F
T
F










F
F
T










F
F
F











© 2007 Elizabeth E. K. Jones and the ASU Department of Mathematics and Statistics - All rights reserved.