Syllogisms

Translate into sets#

“All poets are writers” places the poet set inside the writer set. It does not say all writers are poets.

“No poets are robots” separates those sets. “Some writers are teachers” establishes at least one member in the overlap.

Test necessity#

A valid conclusion must be true in every arrangement allowed by the premises. Draw simple circles or imagine a counterexample.

From “All A are B” and “All B are C,” it follows that all A are C. From “Some A are B” and “All B are C,” it follows that some A are C.

Avoid existence assumptions#

Universal statements do not always establish that members exist. Under standard test conventions, follow the stated rules carefully and do not create a “some” conclusion from only universal premises unless existence is given.

Common mistakes#

Do not reverse “all.” Do not use real-world knowledge to fill missing links. Two groups both inside a larger group need not overlap.

Final check#

Translate every statement, draw only required relationships, and try to construct an allowed diagram where the proposed conclusion is false. If one exists, the conclusion does not necessarily follow.