Analyzing Arguments - Example

Define the necessary symbols, rewrite the argument in symbolic form, and use a truth table to determine whether the argument is valid.  If the argument is invalid, interpret the specific circumstances that cause the argument to be invalid.

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.

Hypothesis 1:
 If you are not in a hurry, you eat at Lulu's Diner
Hypothesis 2:
 If you are in a hurry, you do not eat good food
Hypothesis 3:
 You eat at Lulu's.
Conclusion:
 Therefore, you eat good food.


p:  You are in a hurry.
q:  You eat at Lulu's.
r:  You eat good food.

H1:
H2:
H3:
 q
C:
 r


p
 q
 r
 ~p
 q*
 H1:  ~r
 H2:  H3:  q*
 r*
T
 T
 T
 F
 T
 T
 F
 F
 F
 T
 F
 T
 T
T
 T
 F
 F
 T
 T
 T
 T
 T
 T
 T
 F
 F
T
 F
 T
 F
 F
 T
 F
 F
 F
 F
 F
 T
 T
T
 F
 F
 F
 F
 T
 T
 T
 T
 F
 F
 F
 T
F
 T
 T
 T
 T
 T
 F
 T
 T
 T
 T
 T
 T
F
 T
 F
 T
 T
 T
 T
 T
 T
 T
 T
 F
 F
F
 F
 T
 T
 F
 F
 F
 T
 F
 F
 F
 T
 T
F
 F
 F
 T
 F
 F
 T
 T
 F
 F
 F
 F
 T
*These columns are optional.

p
 q
 r
 ~p
 q*
 H1:  ~r
 H2:  H3:  q*
 r*
T
 T
 F
 F
 T
 T
 T
 T
 T
 T
 T
 T
 F
The argument is not valid when you are in a hurry, you eat at Lulu's, and you do not eat good food.

p
q
r
~p
q*
H1:  ~r
H2:  H3:  q*
r*
F
 T
 F
 T
 T
 T
 T
 T
 T
 T
 T
 F
 F
The argument is also not valid when you are not in a hurry, you eat at Lulu's, and you do not eat good food.