This is part of a Brazilian test - those are common for enrolling in free higher education or working in public positions. IMO one of the most vile ways of wasting the young generation's potential, as you need to be really smart to pass those exams (think 1-10000 candidate/position ratio) but too stupid to accept the position (think $500 USD monthly salary).

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.

That's why I always use parentheses, i.e. I never rely on operator precedence. Therein lie troubles, lad.

And, as usual, the xkcd is fantastic.