Syllogism Flashcards

Statements: All pens are books. Some books are chairs. Conclusions: I. Some pens are chairs. II. Some chairs are books. Which conclusion(s) follow?

Answer: Only II follows

Some chairs are books follows directly from 'Some books are chairs'; 'Some pens are chairs' cannot be established without a direct link.

Statements: No cat is a dog. All dogs are animals. Conclusions: I. No cat is an animal. II. Some animals are not cats. Which conclusion(s) follow?

Answer: Only II follows

Since all dogs are animals and no cat is a dog, some animals (dogs) are definitely not cats, so Conclusion II follows; Conclusion I does not necessarily follow.

Statements: All flowers are trees. All trees are roots. Conclusions: I. All flowers are roots. II. All roots are flowers. Which conclusion(s) follow?

Answer: Only I follows

All flowers → trees → roots gives 'All flowers are roots'; reversing a universal affirmative does not give a universal affirmative, so Conclusion II does not follow.

Statements: Some stars are moons. No moon is a planet. Conclusions: I. Some stars are not planets. II. No star is a planet. Which conclusion(s) follow?

Answer: Only I follows

Some stars that are moons cannot be planets (since no moon is a planet), so Conclusion I follows; but some stars may not be moons at all and could be planets, so Conclusion II does not follow.

Statements: All cars are buses. Some buses are trains. Conclusions: I. Some trains are cars. II. Some buses are cars. Which conclusion(s) follow?

Answer: Only II follows

Since all cars are buses, by conversion, some buses are cars (Conclusion II follows); there is no direct link between trains and cars, so Conclusion I does not follow.

Statements: No table is a chair. No chair is a sofa. Conclusions: I. No table is a sofa. II. Some sofas are not tables. Which conclusion(s) follow?

Answer: Neither I nor II follows

Two negative premises yield no definite conclusion; we cannot determine the relationship between tables and sofas, so neither conclusion necessarily follows.

Statements: All keys are locks. Some locks are doors. All doors are windows. Conclusions: I. Some keys are windows. II. Some locks are windows. Which conclusion(s) follow?

Answer: Only II follows

Some locks are doors and all doors are windows, so some locks are windows (Conclusion II follows); there is no path from keys to windows through the given statements, so Conclusion I does not follow.