EXAMPLE
2.2.15 SOLUTION
If I
want to be a lawyer, then I want to study logic.
If I
don't want to be a lawyer, then I don't like to argue.
Therefore,
if I like to argue, then I want to study logic.
Let
p: I want to be a lawyer.
Let
q: I want to study logic.
Let
r: I donŐt like to argue.
The
argument has this form:
Now
we make a truth table.
|
p |
q |
r |
~p |
~r |
p¨q |
~p¨r |
~r¨q |
|
T |
T |
T |
F |
F |
T |
T |
T |
|
T |
T |
F |
F |
T |
T |
T |
T |
|
T |
F |
T |
F |
F |
F |
T |
T |
|
T |
F |
F |
F |
T |
F |
T |
F |
|
F |
T |
T |
T |
F |
T |
T |
T |
|
F |
T |
F |
T |
T |
T |
F |
T |
|
F |
F |
T |
T |
F |
T |
T |
T |
|
F |
F |
F |
T |
T |
T |
F |
F |
There is no row in which the conclusion
is false while every premise is true, so the argument is valid.