| p | q | ~p | q L ~p | p  (q L ~p) |
||
| T | T | |||||
| T | F | |||||
| F | T | |||||
| F | F |
2. There are two statement variables so the truth table will have 4 rows. Start by filling in the four possible combinations of truth values for p and q.
| p | q | ~p | q L ~p | p (q L ~p) |
||
| T | T | |||||
| T | F | |||||
| F | T | |||||
| F | F |
Now use the truth values in column 1 and the definition of ~ to fill in column 3.
| p | q | ~p | q L ~p | p (q L ~p) |
||
| T | T | F | ||||
| T | F | F | ||||
| F | T | T | ||||
| F | F | T |
Now use columns 2 and 3, and the definition of L to fill in column 4.
| p | q | ~p | q L ~p | p (q L ~p) |
||
| T | T | F | F | |||
| T | F | F | F | |||
| F | T | T | T | |||
| F | F | T | F |
Finally, use columns 1 and 4, and the definition of to fill in the final column.