Chapter Three, Tutorial One
Truth Tables

In this tutorial and the next we will show how to write a truth table for a sentence of SL. This will allow us to fully analyze the meaning of such a sentence. Later in this chapter, we will see how to apply truth tables to test, for instance, whether a sentence is logically true or an argument is valid.

To write truth tables for an arbitrary sentence of SL, you will have to know the tables which define the connectives. Below is one table for all five connectives; keep it in mind because it will be all important in the next few tutorials!

 P Q P&Q PvQ P>Q P=Q ~P T T T T T T F T F F T F F F F T F T T F T F F F F T T T

Remember that P and Q are variables ranging over all SL sentences. Thus, the table applies to any sentence of our symbolic language.

Here's a very easy application of our table definition of the connectives. Suppose for definiteness that 'B' and 'C' continue to mean that Bob will attend law school and that Carola will attend law school and assume that both are TRUE. What can we say about '~B>C'?

MouseOver the sign to pause the demonstration.

First, notice that 'B' and 'C' are both assigned true: the 'T' underneath each indicates this.

 B C (~ B > C)