How do I construct a truth table for (p v q)->~p

To construct a truth table for the logical expression (p v q) -> ~p, follow these steps:

Step 1: Create the headings for the truth table.
- List all the variables involved, in this case, p and q.
- Write the expression you want to evaluate as the final column heading, which is (p v q)->~p.

Step 2: Determine the number of rows needed.
- Since there are two variables (p and q), there are four possible combinations of truth values (2^2 = 4). So the truth table will have four rows.

Step 3: Fill in the truth values for p and q.
- In the first two columns, assign all possible truth values (T and F) to each variable. Start by repeating each truth value twice, then alternate them. This pattern ensures that each variable takes every possible combination of T and F once.

| p | q | (p v q)->~p |
|---|---|------------|
| T | T | |
| T | F | |
| F | T | |
| F | F | |

Step 4: Evaluate the expression.
- To evaluate the expression (p v q)->~p, break it down into smaller sub-expressions:
i. (p v q) represents the logical OR of p and q.
ii. ~p represents the negation of p.

- Evaluate (p v q) by applying the OR operator to the truth values of p and q. Place the resulting truth value in the corresponding row.

| p | q | (p v q)->~p |
|---|---|------------|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |

- Finally, evaluate ~p by negating the truth value of p. Place the resulting truth value in the final column.

| p | q | (p v q)->~p |
|---|---|------------|
| T | T | F |
| T | F | F |
| F | T | T |
| F | F | T |

Step 5: Finish the truth table.
- Complete the truth table by filling in the remaining rows with the evaluated truth values.

| p | q | (p v q)->~p |
|---|---|------------|
| T | T | F |
| T | F | F |
| F | T | T |
| F | F | T |

That's it! You have now constructed the truth table for the logical expression (p v q)->~p.