EXAMPLE 2.3.9
Test the validity of the following argument.

I have my keys or I'm locked out.
I'm not locked out.
Therefore, I have my keys.



EXAMPLE 2.3.9 Solution

Step 1: Symbolize the argument.

Let p be the statement "I have my keys."
Let q be the statement "I'm locked out."

Then the argument has this form:



Step 2: Make a truth table having a column for each premise and for the conclusion.



Step 3: Look for the indication of an INVALID argument (a row where every premise is true while the conclusion is false).



Notice that there is no row in which the conclusion is false while both premises are true. The absence of such a "bad row" indicates that this argument is VALID.