Your set-inclusion line seems to be inverted to me. I would write:
unhandled failures⊂ failures⊂ undefs⊂ falses
That is to say, "the set of unhandled failures is a proper subset of the set of failures, that is a proper subset of the set of undefined values, that is a proper subset of false values".
Because "" is a false value, but none of the others, undef is an undefined value and a false value but none of the others, etc...