I'm not sure I understand your problem, but my guess goes something like this:
#!/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";
}
}
Outputs (complete with intermediate calculations):
(
"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'