I'd highly recommend the Perl Cookbook by O'Reilly. It answers this and many other questions.

Your question is answered on page 106 in section 4.6 as follows:

#  Store each of the 'sterren' elements into the hash FirstGroup.

foreach $Element ( @sterren ) { $FirstGroup{ $Element } = 1; }

#  If any of the sterren elements also exist in array politici,
#  store that value into the hash 'Both'.

foreach $Element ( @politici )
{
  if ( $FirstGroup{ $Element } ) $Both{ $Element } = 1;
}

#  Finally (this step may or may not be necessary depending on what
#  you want to do) store the keys back into an array.

@Result = keys %Both;
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"Excellent. Release the hounds." -- Monty Burns.