Build a Syllogism
Barbara and Darii are medieval mnemonic names: their vowels give the three statements' types in order (A = All, E = No, I = Some, O = Some ... not), so Barbara is All-All-All and Darii is All-Some-Some. See Wikipedia's syllogism article for the rest of the names. The invalid preset just gets a plain descriptive name.
Shaded: the premises force this region empty. X: a premise says at least one of the two marked regions has a member — shown at the boundary between them when the premises don't say which.
How It Works
Each term gets a circle, and the three circles' overlaps divide the page into 8 regions — every combination of being inside or outside each of the three circles. A statement like "All A are B" or "Some A are not B" only ever talks about two of the three terms, so it always marks exactly two of those regions: the two that agree on the terms it names and differ on the term it doesn't mention.
A universal statement ("All", "No") shades both of its regions, meaning the premises say outright that nothing can be there. A particular statement ("Some", "Some ... are not") marks its two regions with an X, meaning at least one of them has a member — but not necessarily both, and the diagram doesn't yet know which. If the other premise has already shaded one of those two regions, the X moves onto the other one. The conclusion follows exactly when every way of filling in the diagram that satisfies both premises also satisfies the conclusion.
This checker uses the modern reading of "All" and "No", with no existential import: "All A are B" only claims that A minus B is empty — it does not assume A has any members at all.