Construct a truth table for p----> ~q
I'm assuming you're trying to say "if p, then not q".
For this, the table should go like this:
P Q ~Q P => ~Q
T T F F
T F T T
F T F T
F F T T
The spacing got messed up...
The first column is for P
Second is for Q
Third is for ~Q
and the last is for P => ~Q
To construct a truth table for the logical expression "p → ~q", we need to consider all possible combinations of truth values for the propositional variables p and q.
First, let's consider the truth values for p and q. Since there are two variables, each variable can have two possible truth values: true (T) or false (F).
Next, we need to determine the truth value of the expression "p → ~q" for each combination of truth values.
The expression "p → ~q" is a conditional statement, which means it evaluates to true (T) unless the antecedent (p) is true and the consequent (~q) is false.
Here's how we can construct the truth table:
Step 1: List all possible combinations of truth values for p and q.
```
p | q | ~q
---------
T | T | F
T | F | T
F | T | F
F | F | T
```
Step 2: Evaluate the expression "p → ~q" for each combination.
```
p | q | ~q | p → ~q
-------------------
T | T | F | F
T | F | T | T
F | T | F | F
F | F | T | T
```
Therefore, the resulting truth table for the logical expression "p → ~q" is:
```
p | q | ~q | p → ~q
-------------------
T | T | F | F
T | F | T | T
F | T | F | F
F | F | T | T
```
This table shows all possible combinations of truth values for p and q, and the corresponding truth value for the expression "p → ~q".