(a) Use a sequence of logical equivalences to show that (pq)(rs) is logically equivalent to p(q(rs)) (b) Use truth tables to show that (pq)(rs) is logically equivalent to p(q(rs)). (12 points) A cat, a dog, a frog and a pig are all accused of robbing the bank. The police have deduced the following: Statement 1 At least two of the animals are guilty. Statement 2 If the cat is guilty then the dog is innocent or the frog is innocent (but not both.) Statement 3 If the pig is guilty or the frog is guilty (or both) then the dog is innocent. Statement 4 If the pig is guilty then the frog and the cat are both innocent. (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 you find out that the cat and the dog are best friends and that they are always together. (Same as before:) With this new information, 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.)