4. Since there are three statement variables, the truth table will have 8 rows. Start by filling in the eight different combinations of truth values for p, q and r.
| p | q | r | p V q | p V r | ~(p V r) | (p V q) L ~(p V 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 |
Now fill in columns 4, 5 and 6 using the truth tables for V and ~.
| p | q | r | p V q | p V r | ~(p V r) | (p V q) L ~(p V r) | ||
| T | T | T | T | T | F | |||
| T | T | F | T | T | F | |||
| T | F | T | T | T | F | |||
| T | F | F | T | T | F | |||
| F | T | T | T | T | F | |||
| F | T | F | T | F | T | |||
| F | F | T | F | T | F | |||
| F | F | F | F | F | T |
Now use columns 4 and 6 and the truth table for L to fill in the final column. Think of (truth value in column 4) L (truth value in column 6), to find the truth values for each row in the final column.