Construct a truth table for the statement.
(p ↔ q) → p
To construct a truth table for the statement (p ↔ q) → p, we need to consider all possible combinations of truth values for p and q.
There are two variables, p and q, which can each take on two possible truth values: true (T) or false (F). This gives us a total of 4 possible combinations of truth values:
1. When p is true (T) and q is true (T):
- (p ↔ q) → p
- (T ↔ T) → T
- T → T
- T
2. When p is true (T) and q is false (F):
- (p ↔ q) → p
- (T ↔ F) → T
- F → T
- T
3. When p is false (F) and q is true (T):
- (p ↔ q) → p
- (F ↔ T) → F
- T → F
- F
4. When p is false (F) and q is false (F):
- (p ↔ q) → p
- (F ↔ F) → F
- T → F
- F
Now we can summarize the truth table for the statement (p ↔ q) → p:
| p | q | (p ↔ q) → p |
| --- | --- | ----------- |
| T | T | T |
| T | F | T |
| F | T | F |
| F | F | F |
In this truth table, the column (p ↔ q) → p shows the resulting truth value for the statement (p ↔ q) → p for each combination of truth values for p and q.