T4.1: 4 of 4 We have been reviewing basic symbolizations from chapter two. Part of
the point here is that so Back in chapter two, though, we saw that there were certain connectives,
non-truth functional ones, which could
However, it's worth pointing out that Think about the following table for a "mystery" sentence-form '???':
The unknown sentence-form must be true only on the first and third rows. So, what is it? That is, what sentence-form will have exactly this truth table? Before reading on, think for a moment about what it might be. |

In fact, there are *lots* of SL forms which have exactly the truth table
above – they express the truth function which is true just when P
and R are both true.

The first form that may come to mind is P&R. Notice that this is true in exactly rows one and three.

But others are possible. Think just a moment about a longer way of symbolizing the same thing.

To do this, first notice that (P&Q)&R is true on exactly the first row of our table. Right?

Second, what sentence-forms are true on exactly the third row? One that is is (P&~Q)&R. (You can tell, because this just states the partial truth value assignment that defines row three.)

Then just put these two together to form a sentence which says "I'm true on row one or row three":

[(P&Q)&R]v[(P&~Q)&R]

This, like P&R,
is a sentence-form constructed to be true on just the first and third row.
Now, make sure you notice how we constructed it: ** each bracketed expression
represents one of the true rows**. The main connective is a wedge. Now,
this construction procedure will work for any sentence. You may want to try
it for the following final problem...

Give a sentence-form with the following table:

P | Q | R | ??? | |

T | T | T | T | |

T | T | F | F | |

T | F | T | F | |

T | F | F | F | |

F | T | T | F | |

F | T | F | F | |

F | F | T | F | |

F | F | F | T |

Enter your answer in the following field and press TAB or the "Enter" button. (You must type in the sentences 'P', 'Q', and 'R' instead of variables 'P','Q' and 'R'.)