1. (12 points) A cat, a dog, a frog and a pig are all accused of robbing the bank. The police have deduced the following: 2 If the cat is not guilty then the dog is guilty The cat is not guilty if and only if the frog is guilty. The dog is not guilty implies that the pig is guilty. The pig is guilty if the cat is not guilty. (a) Determine if the police Have enough information to be certain who was involved in the robbery and who was not involved in the robbery. . Do not have enough information to be certain who was involved in the robbery and who was not involved in the robbery. Have conflicting information (in other words, the statements are not consistent.) (To show your work, either construct a truth table or use logical equivalences to justify your answer.) (b) Now, suppose that the pig comes forward and admits to being involved with the robbery. (Same as before) With this new information, determine if the police llave enough information to be certain who was involved in the robbery and who was not involved in the robbery. . Do not have enough information to be certain who was involved in the robbery and who was not involved in the robbery. Have conflicting information in other words, the statements are not consistent.) (To show your work, either construct a truth table or use logical equivalences to justify your answer.)