(20 marks) Consider the following scenario, S : I have a rule that no cats are allowed to walk on any tables. My dining-room table has paw prints on it, all of which are from a cat. The only way paw prints can get on a table is by a pet walking on it. All of my pets leave paw prints when they walk. Of all my pets, I only have one cat and she is called Pixel. [10 marks] Represent S in first-order logic. [10 marks] Consider the following statement, P : Pixel has broken my rule. Using your representation of S, apply backward chaining to infer the truth about P. Make sure you show the inference tree and final substitutions