Question 1191579
Here's how we can analyze the statements using symbolic logic and determine who is a knight and who is a knave:

**1. Translation into Propositional Logic:**

Let A, B, and C represent the statements "Al is a knight," "Bob is a knight," and "Carol is a knight," respectively.  Therefore, ¬A, ¬B, and ¬C mean "Al is a knave," "Bob is a knave," and "Carol is a knave," respectively.

* **Al's statement:**  ¬A ↔ C  (Al is a knave if and only if Carol is a knight)
* **Bob's statement:** B ↔ C (Bob is a knight if and only if Carol is a knight)
* **Carol's statement:** ¬A & ¬B (Neither Al nor Bob is a knight)

**2. Truth Table:**

We need to consider all possible truth values for A, B, and C, and see which combinations satisfy all three statements.

| A | B | C | ¬A | ¬A ↔ C | B ↔ C | ¬A & ¬B |
|---|---|---|---|---|---|---|
| T | T | T | F | F | T | F |
| T | T | F | F | T | F | F |
| T | F | T | F | F | F | F |
| T | F | F | F | T | T | F |
| F | T | T | T | T | T | F |
| F | T | F | T | F | F | F |
| F | F | T | T | T | F | T |
| F | F | F | T | F | T | T |

**3. Analysis and Verdict:**

Looking at the truth table, we're searching for a row where *all three* statements (¬A ↔ C, B ↔ C, and ¬A & ¬B) are true.  Only the last row (A=F, B=F, C=F) satisfies all conditions.

* **Row 8:** A is False, B is False, and C is False.

This means:

* Al is a knave (¬A is true).
* Bob is a knave (¬B is true).
* Carol is a knave (¬C is true).

Therefore, Al, Bob, and Carol are all knaves.