I am reading about formulation of equivalent statements.
E.g.
All $A$ are $B$ $\equiv$ There are no $A$ that are not $B$
There is one specific case, that I am a bit confused, specifically the equivalent of the statement
Some $A$ are $B$ e.g. Some people are bigots
The first alternative that I thought about of the statement was:
Not all $A$ are $B$ i.e. Not all people are bigots
This to me seems correct, but the alternative proposed by a solution I am reading is:
There exists at least one A is a B i.e. at least one person is a bigot
So now I am thinking if the statement I came up with is some sort of tautology. I can understand that the proposed expression seems to "convey" more information, but I would like some help to understand if there are any issues with the statement I came up with that are eluding me