is @a4=qw(b g g); considered a subset? If so how about this solution?

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

print "a1, a2 => ",subset(\@a1, \@a2),"\n";
print "a1, a3 => ",subset(\@a1, \@a3),"\n";

sub subset {
        my($a1, $a2)= @_;
        my(%subset);
        @subset{@$a2}=@$a2;
        delete @subset{@$a1};
        return scalar(keys %subset)==0;
}
[download]

It first defines hashkeys for all elements from @a2, then removes all haskeys from @a1. If any haskey remains, @a2 had elements not present in @a1.