Construct a truth table for ~q v ~p.
To construct a truth table for the logical expression "~q v ~p", we need to consider all possible combinations of truth values for the variables 'p' and 'q'.
There are two variables 'p' and 'q', and each variable can have two possible truth values, either true (T) or false (F). Therefore, we will have 2x2 = 4 rows in our truth table, representing all possible combinations of truth values.
Let's start by listing the variables 'p' and 'q', along with their possible truth values, in the first two columns of the truth table:
| p | q | ~q v ~p |
|-----|-----|--------|
| T | T | |
| T | F | |
| F | T | |
| F | F | |
Next, we need to evaluate the expression "~q v ~p" for each combination of truth values.
The negation operator '~' flips the truth value of the variable. So, let's fill in the third column by first evaluating "~q" and then "~p" for each row.
| p | q | ~q v ~p |
|-----|-----|--------|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
Finally, to evaluate the expression "~q v ~p", we use the logical operator 'v' (which stands for logical OR). The result of the logical OR is true (T) if either of the operands is true, otherwise, it is false (F). Let's fill in the truth values for the expression in the last column of the truth table:
| p | q | ~q v ~p |
|-----|-----|--------|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
Therefore, the truth table for the logical expression "~q v ~p" is:
| p | q | ~q v ~p |
|-----|-----|--------|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | T |
Please note that 'v' is the symbol commonly used to represent logical OR, but it can vary in different contexts.