Do note that "! defined $var" is not the same as "! $var".

$ perl -Mstrict -wE '
    my $x;
    say "\$x not defined: ", (! defined $x) ? "Y" : "N";
    say "\$x not TRUE: ", (! $x) ? "Y" : "N";
    $x = 0;
    say "\$x not defined: ", (! defined $x) ? "Y" : "N";
    say "\$x not TRUE: ", (! $x) ? "Y" : "N";
    $x = 1;
    say "\$x not defined: ", (! defined $x) ? "Y" : "N";
    say "\$x not TRUE: ", (! $x) ? "Y" : "N";
'
$x not defined: Y
$x not TRUE: Y
$x not defined: N
$x not TRUE: Y
$x not defined: N
$x not TRUE: N
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