The following question has been asked in the Indian entrance examination "GATE CS 2021", and it has stirred up a lot of confusion regarding how one should interpret "either-or" when coming to logical questions where we are given certain premises and have to determine if something is true via deduction.
Q. Given below are two statements 1 and 2, and two conclusions I and II
Statement 1: All bacteria are microorganisms. Statement 2: All pathogens are microorganisms.
Conclusion I: Some pathogens are bacteria. Conclusion II: All pathogens are not bacteria.
Based on the above statements and conclusions, which one of the following options is logically CORRECT?
- Only conclusion I is correct
- Only conclusion II is correct '
- Either conclusion I or II is correct
- Neither conclusion I nor II is correct
refer this link for the debate - https://gateoverflow.in/357468/gate-cse-2021-set-1-ga-question-9 refer this link for my reasoning - https://gateoverflow.in/357468/gate-cse-2021-set-1-ga-question-9?show=358167#a358167
In short - I feel option D is the correct choice, because neither conclusions follow from the premises, but on the other side a lot of people feel that option C is right because according to them option c is a tautology.
Also there is another confusion regarding the statement of conclusion 2 "All pathogens are not bacteria". Does this mean that there is no pathogen which is also a bacteria, or does it mean there exists some pathogens who are definitely not bacteria? Because when we say a similar statement like "All students are not geniuses", we generally mean that there are only few students who are geniuses, and most of the students are not geniuses. We don't mean to say that there isn't even a single student who is not a genius.
Can anybody please provide an unambiguous, mathematically backed argument for choosing the correct answer, or is the given question and options inherently ambiguous?