1976 AHSME Problem 11

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"?

\begin{array}{l}\textbf{I. }\text{"If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha has purple eyes."}\\ \textbf{II. }\text{"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."}\\ \textbf{III. }\text{"If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha does not have purple eyes."}\\ \textbf{IV. }\text{"The pink elephant on planet alpha does not have purple eyes, or the wild pig on planet beta does not have a long nose."}\end{array}

\textbf{(A) }\textbf{I. }\text{and }\textbf{II. }\text{only}\qquad \textbf{(B) }\textbf{III. }\text{and }\textbf{IV. }\text{only}\qquad \textbf{(C) }\textbf{II. }\text{and }\textbf{IV. }\text{only}\qquad \textbf{(D) }\textbf{II. }\text{and }\textbf{III. }\text{only}\qquad \textbf{(E) }\textbf{III. }\text{only}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.