Construct a truth table for the statement.
(p ↔ q) → p
To construct a truth table for the given statement, we will analyze all possible combinations of the truth values of propositions p and q.
Step 1: Identify the number of rows needed in the truth table.
Since we have two propositions p and q, each with two possible truth values (true or false), we will need 2^2 = 4 rows in our truth table.
Step 2: Create a column for each proposition.
Create two columns, one for p and one for q.
Step 3: Determine the truth values for propositions p and q.
In the truth table, list all possible combinations of truth values for p and q. We will start with both propositions being true and then go through all the possible combinations.
```
| p | q |
|---|---|
| T | T |
| T | F |
| F | T |
| F | F |
```
Step 4: Create a column for the expression (p ↔ q).
To evaluate the expression (p ↔ q), calculate the biconditional (if both p and q are true or both p and q are false, it will be true; otherwise, it will be false).
```
p ↔ q = [(p → q) ∧ (q → p)]
```
```
| p | q | p ↔ q |
|---|---|-------|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
```
Step 5: Evaluate the expression [(p ↔ q) → p].
Now evaluate the conditional statement [(p ↔ q) → p] by comparing the truth value of (p ↔ q) with the truth value of p.
```
| p | q | p ↔ q | (p ↔ q) → p |
|---|---|-------|-------------|
| T | T | T | T |
| T | F | F | T |
| F | T | F | T |
| F | F | T | F |
```
The resulting truth table demonstrates the truth values of the statement (p ↔ q) → p for all possible combinations of the truth values of p and q.