Construct a truth table for the statement.
(p ↔ q) → p
This time, you try.
T T T
T F F
F T F
F F T
I think the 3rd row is incorrect??
You got only the first row correct.
By the way, the truth table you typed here is the one for p <--> q, not (p <--> q) --> p.
To construct a truth table for the statement "(p ↔ q) → p," follow these steps:
1. Start by creating columns for p, q, p ↔ q, and finally for the entire statement (p ↔ q) → p.
2. Write down all possible combinations of truth values for p and q. Since there are two variables, there will be four possible combinations: p = true and q = true, p = true and q = false, p = false and q = true, and p = false and q = false.
3. Fill in the p and q columns with these truth values for each combination. For example:
| p | q |
|---|---|
| T | T |
| T | F |
| F | T |
| F | F |
4. Calculate the truth value of p ↔ q for each combination. The statement p ↔ q is true only when p and q have the same truth value (both true or both false). Fill in the column for p ↔ q accordingly:
| p | q | p ↔ q |
|---|---|-------|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
5. Finally, calculate the truth value of the entire statement (p ↔ q) → p. The conditional statement "if A, then B" is false only when A is true and B is false. Fill in the column for (p ↔ q) → p based on this evaluation:
| p | q | p ↔ q | (p ↔ q) → p |
|---|---|-------|-------------|
| T | T | T | T |
| T | F | F | T |
| F | T | F | T |
| F | F | T | F |
This completes the truth table for the statement "(p ↔ q) → p."