I think that grep is not the right tool for doing what you want. If I am right you want to iterate over all the items in array a and see if they are present in array b. Try the following:

my @SupportedPTs = ('Accounting','Dnd','Essay','FITB','Hotspot','Match
+ing','MC','Narrative','SingleAnswer','SelfGradingGeneric','Sketch','S
+tatic','TF');
my @ProblemTypes = ('Accounting','Dnd','test');

my %seen = ();
foreach (@ProblemTypes) {
    $seen{$_} = 1;
}
for (@SupportedPTs){
  if (! $seen{$_}){
    print "$_  is supported\n";
  } else {
    print "$_ is not supported\n";
  }
}
[download]

Outputs:

Accounting is not supported
Dnd is not supported
Essay  is supported
FITB  is supported
Hotspot  is supported
Matching  is supported
MC  is supported
Narrative  is supported
SingleAnswer  is supported
SelfGradingGeneric  is supported
Sketch  is supported
Static  is supported
TF  is supported
[download]

Update:If you want to use grep (a solution less efficient than the previous), you don't need the temporary hash:

for my $sPT (@SupportedPTs){
  if (! grep{/$sPT/} @ProblemTypes){
     print "$sPT  is supported\n";
   } else {
     print "$sPT is not supported\n";
   }
 }
[download]

Hope this helps,

citromatik