print "Exists\n" if exists $array{$key}; print "Defined\n" if defined $array{$key}; print "True\n" if $array{$key};
A hash element can be TRUE only if it's defined, and defined if it exists, but the reverse doesn't necessarily hold true.
Note that the EXPR can be arbitrarily complicated as long as the final operation is a hash key lookup:
if (exists $ref->[$x][$y]{$key}) { ... }