Solution to Example 2

Use a truth table to test the validity of the following argument.

If you are a hound dog, then you howl at the moon.
You don't howl at the moon.
Therefore, you aren't a hound dog.

A. Valid
B. Invalid

Step 1

Symbolize the argument.

Let p be the statement "You are a hound dog."
Let q be the statement "You howl at the moon."

Then the argument has this symbolic form:

Step 2

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

Step 3

Interpret the truth table.
Notice that in this truth table, there is NO ROW in which conclusion is FALSE while both premises are TRUE.
This tells us that the argument is VALID.

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