smc

The following statements are all logically equivalent. I. P implies Q (pink elephant on planet alpha has purple eyes ---> wild pig on planet beta does not have a long nose) III. Not Q implies not P (contrapositive) IV. Not P nor Q (inverse) I is the given statement, so III and IV work. The answer is $\boxed{\text{III. }\text{and }\text{IV. }\text{only}}.$