my %seen = ();
$seen{$_} = 1 for (@ProblemTypes);
delete $seen{$_} for (@SupportedPTs);
if (%seen) {
  # some element in @ProblemTypes is not in @SupportedPTs
  print "elements in ProblemTypes but not in SupportedPTs: ", join(' ', keys %seen), "\n";
}