Unless I have seriously misunderstood you, the following should suffice.

#!/usr/bin/perl -l

use strict;
use warnings;

my $test1  = [ 'A', 'D', 'B' ];
my $test2  = [ 'A', 'C', 'B' ];
my $source = [ 'A', 'B', 'C', 'A', 'B' ];

print "yes 1" if check_array( $test1, $source );    # Should return Fa
+lse
                                                    # since "D" doesn'
+t exist in
                                                    # $source

print "yes 2" if check_array( $test2, $source );    # Should return Tr
+ue
                                                    # since all elemen
+t exist in
                                                    # $source

sub check_array {
    my ( $test, $source ) = @_;

    my %exists = map { $_ => 1 } @$source;
    foreach my $ts ( @{$test} ) {
        return if ! $exists{$ts};
    }

    return 1;
}
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