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).

 B C [~ B v ~ C] T T T F F T F F

MouseOver the MouseOver the sign to pause the demo.