If the statement "Some professors are spiritualists" is given as true. Which…

Concept

A categorical proposition describes how two classes overlap or exclude one another. A particular affirmative, “Some S are P,” asserts that at least one member lies in both S and P.

An immediate inference to falsity is available only when a proposed statement directly contradicts that asserted overlap; statements about other members remain undetermined.

Application

1. Let P be the set of professors and S the set of spiritualists. The premise gives at least one person x with x in P and x in S, so the intersection P ∩ S is non-empty.

2. The statement “No professors are spiritualists” requires P ∩ S to be empty. The same intersection cannot be both non-empty and empty, so that universal negative is false.

Contrast

• “All professors are spiritualists” makes a claim about every professor; the premise confirms only at least one, so the universal claim is not settled.

• “Some professors are not spiritualists” requires another professor outside the overlap; the premise supplies no information about all remaining professors.

• “Some spiritualists are not professors” requires a spiritualist outside the professor set; the premise supplies no information about spiritualists outside the overlap.

Cross-check

A one-circle overlap witness is enough: place one person in both sets. That witness satisfies “Some professors are spiritualists” and immediately violates “No professors are spiritualists.”

Result

Therefore, “No professors are spiritualists” is the statement that can immediately be inferred to be false.