# initialize all sets to be empty
@union = @intersection = @difference = ();
%count = ();

# count the number of times each unique element appears
# in both arrays
foreach $element (@array1, @array2) { $count{$element}++ }

# for each unique element, determine whether it belongs
# to the union, intersection, or difference of the original arrays
foreach $element (keys %count) {

    # since the union includes all elements present in either
    # array, every unique element should belong to the union
    push @union, $element;

    # if this element occurred appeared more than once
    # (i.e., in both arrays), then it belongs to the intersection.
    # if it occurred only once (i.e., in only one array), then it
    # belongs to the difference.  perlfaq4 explains that this is
    # -symmetric difference-, like an XOR operation.
    push @{ $count{$element} > 1 ? \@intersection : \@difference }, $element;
}