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'?

Click here to see the demonstration applying the truth table definitions.

MouseOver
the sign to
** pause** the demonstration.

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