Assumptions:
(1) - You need to assume that the options "full-time" and "part-time" are exhaustive in so far as there is no excluded middle
(2) - You must also assume that it is possible that there is more than one office
(3) - There exists employees in the NY office (*)
Without these assumptions it is impossible to solve the question
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Approaching it rigorously, the question supposes that the answer MUST be true, i.e. it is necessarily true given the information. Therefore, to eliminate an option, one need only conceive of a scenario in which the answer is false, yet the information is true:
- A: It is possibly false that 'all full-time employees work in the NY office', since it possible that there is another office (assumption 2) and that full time employees work there, this doesn't imply any contradiction with the data
- B: It is necessarily false that all employees that work in the NY office are part time, since by the data there are no employees who work part time
- C: Suppose for sake of reductio that it is false that "all employees in the NY office work full-time", using assumption (1), then there must be some employees who work in the NY office who are part time (assumption 3), but this contradicts the original statement. However the original statement is true, therefore it is false that it is false that "all employees in the NY office work full-time", meaning it is true.
- D: This directly contradicts the information, as if it were true that some employees work in the NY office part time, then this contradicts "no part time employees work in NY"
- E: This is possibly false, since we can suppose the falsity of the statement "No full-time employees work in any office except the NY office" by conceiving of FT employees working out of NY, with no contradiction to the information. Moreover, A and E imply each other, and since only 1 answer is correct, if A was correct, then E would be, and if E was correct, A would be. But neither case can be true since there is only 1 correct answer, therefore neither A or E is correct.
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(*) this assumption however is merely due to the ambiguity of the language, if option C stated "if there existed employees in NY, then they are full time" then this assumption can be dispensed with