3. Since there are two statement variables, the truth table will have 4 rows. Start by filling in the four different combinations of truth values for p and q.
| p | q | p V q | ~p | (p V q) L ~p | ||
| T | T | |||||
| T | F | |||||
| F | T | |||||
| F | F |
Now fill in columns 3 and 4, using the truth tables for V and ~.
| p | q | p V q | ~p | (p V q) L ~p | ||
| T | T | T | F | |||
| T | F | T | F | |||
| F | T | T | T | |||
| F | F | F | T |
To fill in the final column, think of (value in column 3) L (value in column 4), and use the truth table for L. For example, the first row of the last column will be F since T L F is F.