Why all the hashes? Array lookups are faster, no? Plus this way you have no extra arrays hanging around. First argument to issubset() is a ref to the big set, second argument is a ref the alleged subset:

#!/usr/bin/perl

use strict;

my @a1=qw(a b c d e f g);
my @a2=qw(b g);
my @a3=qw(c d e f g h);

sub issubset
{
   ($a,$b)=@_;
   for my $x (@$b)
      {
      return ("not a subset") unless grep {$x eq $_} @$a;
      }
   return ("a subset");
}

print "a2 is ",issubset(\@a1,\@a2)," of a1\n";
print "a3 is ",issubset(\@a1,\@a3)," of a1\n";

__END__
Output is:
a2 is a subset of a1
a3 is not a subset of a1
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HTH