Q) Given the statement here. Which of these conclusions logically follow:
Statement: All A are B.
Conclusions:
- All A are B
- Some A are B
- All A being B is a possibility
- Some A being B is a possibility
The question below was asked in an Indian entrance exam. (for recruiting Clerks)
The problem with this question is the answers are being disputed by the teachers themselves, and they do not get into a consensus on an answer to this question.
Your Expert view on this problem will greatly be appreciated.
Sorry for not including the view of some teachers. I am including it below.
Edit: Some teachers argue that the conclusion 3 & 4 do not follow, since all they argue as follows "Since All A are B is true, All A being B is a possibility is false, since if it(3rd statement) were true, that would implicitly mean All A being B can sometimes be false, but it is not so, So it must be false. Hence they Argue that the statement 3 does not follow.(They give a similar reasoning for the "fallacy" of 4th conclusion)
My View is that the statements 4 trivially follow(and 3 by a similar reasoning), since $$\text{All A are B }\implies \exists \text{an element in A which is B} \implies \text{The possibility of some A being B}$$
All 4 are logical conclusions.
Only the first is equivalent to the original statement.
To understand why the first is the correct correct answer,
let's put some flesh on the statement and consider connotations.
All politicians are human. That is a fact.
Some politicians are human. Still a fact but slanders the
profession by connotating only some politicians are human.
It is possible all politicians are human. Still a fact but
still has a connotation of some inhuman politicians.
It is possible some politicians are human. This describes
the current situation in US national politics.