If we're going against two separate files here, it might not be most efficient to slurp each file up, and do our comparisons against the file's contents. Something like the following might be more efficient:

sub check_file {
   my $filename = shift;
   my $string = shift;

   open(F, "< $filename") or die "$filename: $!";
   while(<F>) {
      close(F), return 1 if /\Q$string\E/;
   }
   close(F);
   return
}

if (search_file('file1', 'string1') &&
    search_file('file2', 'string2'))
{
   print "OK\n";
} else {
   print "No\n";
}
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The question title itself is referring to arrays, in which case the other responses would be more appropriate, but the question itself has to do with file contents, so I thought I'd throw this out there.