construct a truth table for(p^~q)________> q .
To construct a truth table for the given expression (p^~q) --> q, we need to consider all possible combinations of truth values for the variables p and q and then evaluate the expression for each combination.
Here are the steps to construct the truth table:
1. Create a table with columns for p, q, (p^~q), and (p^~q) --> q.
2. In the p column, list all possible truth values for the variable p. In this case, there are 2 possibilities: True (T) and False (F).
3. In the q column, list all possible truth values for the variable q. Again, there are 2 possibilities: True (T) and False (F).
4. Calculate the value of (p^~q) for each combination of p and q.
To compute (p^~q), first evaluate ~q for each value of q. The ~ (not) operator negates the truth value of q. So, if q is True (T), ~q would be False (F) and vice versa.
Next, evaluate p^~q by applying the ^ (and) operator. The ^ operator yields True (T) if both p and ~q are True (T), otherwise it yields False (F).
5. Finally, compute the value of (p^~q) --> q. The --> (implication) operator returns False (F) if (p^~q) is True (T) but q is False (F), otherwise, it returns True (T).
Let's construct the truth table step by step:
```
| p | q | ~q | (p^~q) | (p^~q) --> q |
|---|---|----|--------|-------------|
| T | T | F | F | T |
| T | F | T | T | F |
| F | T | F | F | T |
| F | F | T | F | T |
```
Therefore, the completed truth table for (p^~q) --> q is shown above.