This code might help to illustrate what is happening.

$ perl -le '
> print q{Elem.  Exists  Defined True    Value};
> @ny            = ( q{no      }, q{yes     } );
> $arr[ 9 ]      = 9;
> $arr[ 0 ]      = 0;
> $arr[ 1 ]      = q{one};
> @arr[ 3 .. 5 ] = ( undef ) x 3;
> $arr[ 7 ]      = q{};
> print
>    qq{[ $_ ]: },
>    $ny[ exists $arr[ $_ ] ],
>    $ny[ defined $arr[ $_ ] ],
>    $arr[ $_ ] ? $ny[ 1 ] : $ny[ 0 ],
>    $arr[ $_ ]
>    for 0 .. $#arr;'
Elem.  Exists  Defined True    Value
[ 0 ]: yes     yes     no      0
[ 1 ]: yes     yes     yes     one
[ 2 ]: no      no      no      
[ 3 ]: yes     no      no      
[ 4 ]: yes     no      no      
[ 5 ]: yes     no      no      
[ 6 ]: no      no      no      
[ 7 ]: yes     yes     no      
[ 8 ]: no      no      no      
[ 9 ]: yes     yes     yes     9
$
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I hope this is helpful.