5. 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 | ~q | p V q | p L ~q | (p V q) L ~q | ||
| T | T | ||||||
| T | F | ||||||
| F | T | ||||||
| F | F |
Now fill in columns 3 and 4, using the truth tables for V and ~.
| p | q | ~q | p V q | p L ~q | (p V q) L ~q | ||
| T | T | F | T | ||||
| T | F | T | T | ||||
| F | T | F | T | ||||
| F | F | T | F |
Now use columns 1 and 3, and the truth table for L to fill in column 5. Then use columns 4 and 3, and the truth table for L to fill in column 6. Finally, compare columns 5 and 6 to decide if the statements forms p L ~q and (p V q) L ~q are logically equivalent.