How do I interpret this statement from syllogism?

Question

I have a doubt in a particular statement:

"Only A are B".

Now I read it somewhere to interpret it as " All B are A".

How do I relate the two statements? A detailed description about the same will be most welcome.

Answer 1

1. "All B are A."

   $\forall x \;\big(x\in B\implies x\in A\big)$

2. "Only A are B."

   $\forall x \;\big(x\not\in A\implies x\not\in B\big)$

This diagram (notice that $B\subseteq A$) illustrates why sentences $1$ and $2$ are logically equivalent:

Answer 2

"All B are A" is called universal affirmative and is one of four major types of any premise or conclusion in Greek syllogism as referenced here:

There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form (note: M – Middle, S – subject, P – predicate.)...

The premises and conclusion of a syllogism can be any of four types, which are labeled by letters as follows. The meaning of the letters is given by the table:

So for your case, "All B are A" can be expressed using predicate logic as $\forall x (B(x) \to A(x))$ or $\lnot \exists x (B(x) \land \lnot A(x))$, the latter formula can be translated to English as "It's not the case there's some B which is not A". Now perhaps it's easier for you to see this is equivalent to "Only A are B" which seemingly doesn't belong to any of the above 4 major types...