Creating Truth Tables

To create a truth table, first consider the number of individual variables being evaluated -- this is your initial number of columns. Next consider your rows: If you let x equal the number of variables, you will need 2x rows for truth values (not including your header row identifying the variable and/or compound statement). Finally, when entering the truth values for each variable, starting with the first column, alternate T's and F's in groups of 2x-1, decreasing x by one for each successive column.

Suppose you are working with 3 variables; p, q and r. Letting x = the number of variables, you will need 3 columns (x = 3), and 8 rows (2x = 23 = 8) for truth values. Now to enter the truth values: Starting with p, alternate with 4 T's and 4 F's (2x-1 = 22 = 4), then alternate by 2's for the q column (2x-2 = 21 = 2; starting to get the picture?), and finally alternate every other row with T and F (20 = 1) for the r column, so that your truth table now looks like this:

 p q r T T T T T F T F T T F F F T T F T F F F T F F F