construct a truth table for p_____> ~q

To construct a truth table for the logical expression "p → ~q," we need to analyze all possible combinations of truth values for the variables p and q.

Let's start by listing all the possibilities for p and q and then calculating the corresponding value for "p → ~q."

1. p = true, q = true:
p → ~q = true → ~true = true → false = false

2. p = true, q = false:
p → ~q = true → ~false = true → true = true

3. p = false, q = true:
p → ~q = false → ~true = false → false = true

4. p = false, q = false:
p → ~q = false → ~false = false → true = true

Now, we can summarize the results in a truth table:

| p | q | ~q | p → ~q |
|---|---|-----|--------|
| T | T | F | F |
| T | F | T | T |
| F | T | F | T |
| F | F | T | T |

In the truth table above, T stands for true, F stands for false, and ~q denotes the negation of q.