short question, short answer:

my @words = qw/foo bar/; #your @A
my @strings = <DATA>; #your @B

my $contains = 0; # a boolean
{
   my $words = join '|',map quotemeta,@words;
   for(@strings){
         ++$contains and last if /$words/;
   }
}

print $contains ? 'yes' : 'no' , "\n"
__DATA__
abc def
ghi foo
jkl mno
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To get a better answer: what does "array @B contains the words in array @A" mean? In which case is this fullfilled? I have assumed that one element of @B must contain one element of @A...

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