EXAMPLE 2.2.13 SOLUTION
Let p: ÒI got a
scholarshipÓ
Let q: ÒI got an
ÔAÕ in math.Ó
Let r: ÒIÕm not
good at logic.Ó
The argument has
this form:
Now we make a
truth table:
|
p |
q |
r |
~p |
~r |
pôq |
ròq |
~rò~p |
|
T |
T |
T |
F |
F |
T |
T |
F |
|
T |
T |
F |
F |
T |
T |
T |
T |
|
T |
F |
T |
F |
F |
F |
T |
F |
|
T |
F |
F |
F |
T |
F |
F |
T |
|
F |
T |
T |
T |
F |
F |
T |
T |
|
F |
T |
F |
T |
T |
F |
T |
T |
|
F |
F |
T |
T |
F |
F |
T |
T |
|
F |
F |
F |
T |
T |
F |
F |
T |
We see that in
the first row the conclusion is false while both premises are true. The argument is INVALID.