T3.2Full Tables p1

Chapter Three, Tutorial Two
Full Truth Tables

In the last tutorial, we determined the truth values of SL sentences when the truth values for all atomic components were given. But we don't always know the truth values of atomic components. For instance, we do not know who Bob and Carola are. What we can say is that '~Bv~C' is false if 'B' and 'C' are true. That is, it is possible that both will be law students, and if that possibility holds, then '~Bv~C' is false.

A truth table is our way of going through all such possibilities at once:

	B	C
row one:	T	T
row two:	T	F
row three:	F	T
row four:	F	F

Instead of doing one row, i.e., one possibility, we can go through all possibilities at once when constructing a truth table. That way we don't have to assume we know which of 'B' and 'C' are true.

The following demonstration applies our truth table definitions and the reasoning of tutorial one, to all possibilities. This is a "full" truth table (i.e., a table going through all possibilities).

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

MouseOver the MouseOver the sign to pause the demo.

First, notice that we have four rows in this table. One for each way in which Bob and Carola is or is not to be a law student.

As usual, we take the truth values assigned on the left and move them under the complex sentence's atomic components.

Then we work on the negated atomic sentences: each negation is assigned the opposite truth value from its atomic component.

Finally, under the main connective, 'v', we write the truth value of the whole sentence. (Each value here is determined by the values of the immediate components, here the two negations.)

Notice that the procedure here is just like what we did in tutorial one, except now we have four rows instead of one. But each of the rows works just like those of the one row tables.

Click here to replay.

When you are finished with this more complex table, move on to the next page.