#3 and #4 say there exists a K for which the interior statement is true. K=2 doesn't make the interior true for either, so choosing it doesn't tell us whether

#3 and #4 say there exists a K for which the interior statement is true. K=2 doesn't make the interior true for either, so choosing it doesn't tell us whether #3 and #4 are true or false. However, if we choose K=1 then we prove #3 and #4 are true.