Problem: Which of the following statements is (are) equivalent to the statement "If the pink elephant on planet alpha has purple eyes, then the wild pig on planet beta does not have a long nose"?
I. "If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha has purple eyes."
II. "If the pink elephant on planet alpha does not have purple eyes, then the wild pig on planet beta does not have a long nose."
III. "If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha does not have purple eyes."
IV. "The pink elephant on planet alpha does not have purple eyes, or the wild pig on planet beta does not have a long nose."
Answer Choices:
A. I and III only
B. II and IV only
C. III only
D. III and IV only
E. II and III only
Solution:
The statements "P implies ," "Not implies not " and "Not or " are equivalent. The given statement, statement III and statement IV are of these forms, respectively.