Construct a truth table for (~pvq) ____>
To construct a truth table for the expression (~pvq) -->, we first need to determine the number of variables involved. In this case, we have two variables - p and q.
The expression (~pvq) is a combination of three logical operations - negation (~), disjunction (v), and implication (-->) - applied to the variables p and q.
To start, we create a truth table with two columns for the variables p and q. Since each variable can have two possible truth values (true or false), we will have two rows in the truth table.
```
| p | q |
-------------
| . | . |
| . | . |
```
Next, we need to evaluate the expression (~pvq) --> for each combination of truth values for p and q.
The negation (~) operator denotes logical negation, so for each row, we negate the value of p and represent it with ¬p.
```
| p | q |
-------------
| ¬p | . |
| ¬p | . |
```
The disjunction (v) operator represents logical OR. We evaluate the OR operation between ¬p and q and write the result in the next column.
```
| p | q |
-------------
| ¬p | ¬p v q |
| ¬p | ¬p v q |
```
Finally, the implication (-->) operator represents logical implication. We evaluate the implication between ¬p v q and write the result in the last column.
```
| p | q | ¬p v q | (~pvq) -->
-------------------------------
| ¬p | ¬p v q | ? |
| ¬p | ¬p v q | ? |
```
To determine the truth value for (~pvq) -->, we need to apply the definition of implication. The implication (~pvq) --> is true when the antecedent (~pvq) is false or when the consequent is true.
```
| p | q | ¬p v q | (~pvq) -->
-------------------------------
| ¬p | ¬p v q | ? | ? |
| ¬p | ¬p v q | ? | ? |
```
To complete the truth table, we need to evaluate the final column using the definition of implication. Since we don't have the specific expression following the implication, we cannot fill in the last column without knowing the complete expression. Please provide the full expression following the implication for further assistance.