MathDB
Logic: Starring Pink Elephant and Wild Pig

Source: 1976 AHSME Problem 11

May 17, 2014
AMC

Problem Statement

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"?
<spanclass=latexbold>I.</span><span class='latex-bold'>I. </span> "If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha has purple eyes."
<spanclass=latexbold>II.</span><span class='latex-bold'>II. </span> "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.
<spanclass=latexbold>III.</span><span class='latex-bold'>III. </span> "If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha does not have purple eyes."
<spanclass=latexbold>IV.</span> <span class='latex-bold'>IV. </span> "The pink elephant on planet alpha does not have purple eyes, or the wild pig on planet beta does not have a long nose."
<spanclass=latexbold>(A)</span><spanclass=latexbold>I.</span>and <spanclass=latexbold>II.</span>only<spanclass=latexbold>(B)</span><spanclass=latexbold>III.</span>and <spanclass=latexbold>IV.</span>only<spanclass=latexbold>(C)</span><spanclass=latexbold>II.</span>and <spanclass=latexbold>IV.</span>only<spanclass=latexbold>(D)</span><spanclass=latexbold>II.</span>and <spanclass=latexbold>III.</span>only<spanclass=latexbold>(E)</span>and <spanclass=latexbold>III.</span>only<span class='latex-bold'>(A) </span><span class='latex-bold'>I. </span>\text{and }<span class='latex-bold'>II. </span>\text{only}\qquad<span class='latex-bold'>(B) </span><span class='latex-bold'>III. </span>\text{and }<span class='latex-bold'>IV. </span>\text{only}\qquad<span class='latex-bold'>(C) </span><span class='latex-bold'>II. </span>\text{and }<span class='latex-bold'>IV. </span>\text{only}\qquad<span class='latex-bold'>(D) </span><span class='latex-bold'>II. </span>\text{and }<span class='latex-bold'>III. </span>\text{only}\qquad <span class='latex-bold'>(E) </span>\text{and }<span class='latex-bold'>III. </span>\text{only}