#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11152381
use warnings;

my %sets = ( A => [1,2,3], B => [3, 4], C => [1, 3, 4] );
use Data::Dump 'dd'; dd 'original sets', \%sets;

my %intersection;
for my $setname ( keys %sets )
  {
  $intersection{$_}{$setname}++ for @{ $sets{$setname} };
  }
use Data::Dump 'dd'; dd 'intersection', \%intersection;

print "items in more than one set:\n";
for my $setname ( sort keys %intersection )
  {
  if( 1 < keys %{ $intersection{$setname} } )
    {
    my $where = join ' and ', map "'$_'",
      sort keys %{ $intersection{$setname} };
    print "    '$setname' is in $where\n";
    }
  }

##</code><code>##

(
  "original sets",
  { A => [1, 2, 3], B => [3, 4], C => [1, 3, 4] },
)
(
  "intersection",
  {
    1 => { A => 1, C => 1 },
    2 => { A => 1 },
    3 => { A => 1, B => 1, C => 1 },
    4 => { B => 1, C => 1 },
  },
)
items in more than one set:
    '1' is in 'A' and 'C'
    '3' is in 'A' and 'B' and 'C'
    '4' is in 'B' and 'C'