Here's another option using smart matching:

use Modern::Perl;

my $a = "AB:APPLE:BOY:ZOO:ZOOM";
my $b = "APPLE:ZOO";
my $c = "BOY:GIRL";

say isSubset( $b, $a );    #Returns 1
say !isSubset( $c, $a );   #Returns 1

sub isSubset {
    my @small = split ':', $_[0];
    my @big   = split ':', $_[1];
    @small ~~ [ grep $_ ~~ @big, @small ];
}
[download]

Update: The subroutine below might be more efficient, since it's not building a list (the results are the same):

sub isSubset {
    my $count = my @small = split ':', $_[0];
    my @big   = split ':', $_[1];
    do { $count-- when @big } for @small;
    !$count;
}
[download]

Here's an interesting read: How fast is Perl's smart match operator for searching scalar in an array?.

UpdateUpdate: Ran a benchmark on three subroutines having different set/subset algorithms:

use Modern::Perl;
use Benchmark qw(cmpthese);

my $a = "AB:APPLE:BOY:ZOO:ZOOM";
my $b = "APPLE:ZOO";
my $c = "BOY:GIRL";

sub isSubset {
    my @small = split ':', $_[0];
    my @big   = split ':', $_[1];
    @small ~~ [ grep $_ ~~ @big, @small ];
}

sub isSubsetSmarter {
    my $count = my @small = split ':', $_[0];
    my @big = split ':', $_[1];
    do { $count-- when @big } for @small;
    !$count;
}

sub isSubsetHash {
    my $count = my @small = split ':', $_[0];
    my %big;
    $big{$_} = 1 for split ':', $_[1];
    do { $count-- if $big{$_} } for @small;
    !$count;
}

cmpthese(
    -5,
    {
        isSubset        => sub { isSubset( $b,         $a ) },
        isSubsetSmarter => sub { isSubsetSmarter( $b,  $a ) },
        isSubsetHash    => sub { say isSubsetHash( $b, $a ) },
    }
);
[download]

Results:

                    Rate      isSubset    isSubsetHash isSubsetSmarter
isSubset        143452/s            --            -15%            -54%
isSubsetHash    169263/s           18%              --            -45%
isSubsetSmarter 309705/s          116%             83%              --
[download]

The original isSubset is the slowest, but isSubsetSmarter is surprisingly the fastest of the crew--at least with these small data sets.

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