Build a truth table for the statement ~(pvq)^~p

To build a truth table for the given statement ~(pvq)^~p, we need to consider all possible combinations of truth values for p and q.

Step 1: Determine the components of the statement
The given statement consists of three components: ~(pvq), ~p, and the overall statement.

Step 2: List all possible combinations of truth values for p and q
Since there are two variables, p and q, there are 2^2 = 4 possible combinations of truth values.

| p | q |
|---|---|
| T | T |
| T | F |
| F | T |
| F | F |

Step 3: Evaluate the components
~(pvq): This component is the negation of the disjunction (pvq). To evaluate this, we consider the disjunction (pvq) and then take the negation of the result.

| p | q | pvq | ~(pvq) |
|---|---|-----|--------|
| T | T | T | F |
| T | F | T | F |
| F | T | T | F |
| F | F | F | T |

~p: This component is the negation of p.

| p | ~p |
|---|----|
| T | F |
| F | T |

Step 4: Calculate the overall statement
The overall statement is the conjunction of ~(pvq) and ~p.

| p | q | pvq | ~(pvq) | ~p | (pvq)^~p |
|---|---|-----|--------|----|----------|
| T | T | T | F | F | F |
| T | F | T | F | F | F |
| F | T | T | F | T | F |
| F | F | F | T | T | T |

Step 5: Write the truth table
Finally, we can compile all the information into a truth table for the given statement ~(pvq)^~p.

| p | q | pvq | ~(pvq) | ~p | (pvq)^~p |
|---|---|-----|--------|----|----------|
| T | T | T | F | F | F |
| T | F | T | F | F | F |
| F | T | T | F | T | F |
| F | F | F | T | T | T |

Answer: The truth table for the statement ~(pvq)^~p is as shown above.