Exercise B

Using the symbolization key given, symbolize each English sentence in TFL.

• $A$:

  Mister Ace was murdered

• $B$:

  The butler did it

• $C$:

  The cook did it

• $D$:

  The Duchess is lying

• $E$:

  Mister Edge was murdered

• $F$:

  The murder weapon was a frying pan

1. Either Mister Ace or Mister Edge was murdered.

2. If Mister Ace was murdered, then the cook did it.

3. If Mister Edge was murdered, then the cook did not do it.

4. Either the butler did it, or the Duchess is lying.

5. The cook did it only if the Duchess is lying.

6. If the murder weapon was a frying pan, then the culprit must have been the cook.

7. If the murder weapon was not a frying pan, then the culprit was either the cook or the butler.

8. Mister Ace was murdered if and only if Mister Edge was not murdered.

9. The Duchess is lying, unless it was Mister Edge who was murdered.

10. If Mister Ace was murdered, he was done in with a frying pan.

11. Since the cook did it, the butler did not.

12. Of course the Duchess is lying!