Question 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”?
$\mathrm{I}.$ “If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha has purple eyes.”
$\mathrm{II}.$ “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.”
$\mathrm{III}.$ “If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha does not have purple eyes.”
$\mathrm{IV}.$ “The pink elephant on planet alpha does not have purple eyes, or the wild pig on planet beta does not have a long nose.”
*The word “or” is used here in the inclusive sense (as is customary in mathematical writing).*
$\mathrm{I}.$ “If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha has purple eyes.”
$\mathrm{II}.$ “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.”
$\mathrm{III}.$ “If the wild pig on planet beta has a long nose, then the pink elephant on planet alpha does not have purple eyes.”
$\mathrm{IV}.$ “The pink elephant on planet alpha does not have purple eyes, or the wild pig on planet beta does not have a long nose.”
*The word “or” is used here in the inclusive sense (as is customary in mathematical writing).*