Syllogism Flashcards

Statements: Some apples are mangoes. All mangoes are grapes. Conclusions: I. All apples are grapes. II. Some grapes are apples. Which conclusion(s) follow?

Answer: Only II follows

Some apples are mangoes and all mangoes are grapes, so some apples are grapes; by conversion, some grapes are apples (Conclusion II follows); 'All apples are grapes' cannot be concluded since only some apples are mangoes.

Statements: All rivers are lakes. No lake is a pond. Conclusions: I. No river is a pond. II. Some ponds are not lakes. Which conclusion(s) follow?

Answer: Only I follows

All rivers are lakes and no lake is a pond, so no river is a pond (Conclusion I follows); Conclusion II states some ponds are not lakes, which is the converse of 'No lake is a pond' and is valid but not a standard necessary conclusion here — Conclusion I definitively follows.

Statements: Some doctors are engineers. Some engineers are pilots. Conclusions: I. Some doctors are pilots. II. Some pilots are doctors. Which conclusion(s) follow?

Answer: Neither I nor II follows

With two particular affirmative premises, no definite conclusion can be drawn; the set of engineers that are doctors may be entirely different from the set of engineers that are pilots.

Statements: All squares are rectangles. No rectangle is a circle. Conclusions: I. No square is a circle. II. Some circles are not rectangles. Which conclusion(s) follow?

Answer: Both I and II follow

All squares are rectangles and no rectangle is a circle, so no square is a circle (I follows); since no rectangle is a circle, some circles are definitely not rectangles (II follows by obversion).

Statements: All gold is silver. Some silver is bronze. Conclusions: I. Some gold is bronze. II. Some bronze is silver. Which conclusion(s) follow?

Answer: Only II follows

Some silver is bronze, so by conversion, some bronze is silver (Conclusion II follows); there is no direct link proving some gold is bronze, so Conclusion I does not follow.

Statements: No bird is a fish. All fish are aquatic. Conclusions: I. No bird is aquatic. II. Some aquatic things are not birds. Which conclusion(s) follow?

Answer: Only II follows

Since all fish are aquatic and no bird is a fish, those aquatic creatures (fish) are not birds, so Conclusion II follows; birds may still be aquatic through other means, so Conclusion I does not definitively follow.

Statements: All planets are stars. All stars are galaxies. Some galaxies are universes. Conclusions: I. All planets are galaxies. II. Some universes are planets. Which conclusion(s) follow?

Answer: Only I follows

All planets → stars → galaxies, so all planets are galaxies (I follows); the galaxies that are universes may be entirely different from galaxies that are stars, so Conclusion II does not follow.