2. A shop owner calls the police to claim robbery. Three suspects A, B, C were identified. The detective in charge could establish the following: P1: The robbery could only have been committed by A or B or C (or a combination of them). P2: If A was guilty then he had exactly one accomplice. P3: If B is innocent, so is C P4: If B or C is guilty then so is A P5: If C is innocent, so is B (a) (5 points) Translate the above premises into logical WFF (where the propositional variable Z meaning Z is guilty) P1 P2 P3 P4 P5 (b) (7 points) Using the 5 statements above as premises, prove that P1 A P2 A P3 A P4 A P5 AUse formal proof methods with line numbers and reasons for each line of your proof. Add lines to the table as needed 2 4 6 Premise (P1 from above) Premise (P2 from above) Premise Premise Premise Page 4, Question 2 con't (c) (4 points) Using the 5 statements above as premises, prove that P1a P2AP3AP4AP5 -B Use formal proof methods with line numbers and reasons for each line of your proof. Add lines to the table as needed. Premise (P1 from above) Premise (P2 from above) Premise Premise Premise 2 4. 5. 6. (d) (4 points) Using the 5 statements above as premises, prove that PIAP2A PSA pan P5-, C Use formal proof methods with line numbers and reasons for each line of your proof. Add lines to the table as needed Premise (P1 from above) Premise (P2 from above) 2 3 4 5 6 Premise Premise