Basically you need to perform a set difference operation.

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";
}
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