They are not even remotely the same.
6÷2(1+2) is written in a deliberately confusing fashion. This is a simple math olympiad-style question. All universal quantifications on the empty set are true, for the same reason that the implication A -> B is true when A is false regardless of B. It cannot be any other way. Precedence of infix operators on the other hand is completely arbitrary, we settled on multiplication before addition because otherwise it would be a pain to write polynomials.
The point is it's an attempt to sucker people into a fight over ambiguity over the natural readings of what looks like informal English (which can vary from person to person) vs formal logic statements predicated on a strict framework which may sound weird but actually have right answers. And it works every damn time.
It might be a math Olympiad question, but a math Olympiad participant is supposed to know how, say, a vacuous truth works, and, moreover the mapping of formal English to logical operators (see also: the inclusive or) and that is not how everyone in the world will parse the statement of the problem.
Is the point here to educate people on a quirk of formal logic, or is a smugbait to promote a book? Oh look, there's a book. Quelle surprise.