Dishrag - No, you are not wrong in trying to relate this to set notation.
The four different types of statements may be understood as statements describing the relationships between sets.
A - Universal Affirmative: All S are P = Set S is a subset of set P
E - Universal Negative: All S are not P = Set S and set P do not intersect
I - Particular Affirmative: Some S are P = Set S and set P intersect
O - Particular Negative: Some S are not P = Set S is not a subset of set P
In Plato's original syllogism (post 43) the conclusion is an E statement (All A are not C) so the answer to your question would be "No, no A can be C."
In post 45 Alglenne seemed to suggest that it could be changed to an O statement (Some A are not C). In that case the answer to your question would be "Yes, some A could be C."