Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: I. All film stars are playback singers. II. All film directors are film stars. Conclusions: I. All film directors are playback singers. II. Some film stars are film directors. A. Only conclusion I follows. B. Only conclusion II follows. C. Neither conclusion I nor II follows. D. Both conclusions I and II follow.

GATE 2015 · General Aptitude · Statements Follow · medium

Answer: D. Both conclusions I and II follow.

1. Check Conclusion I: All film directors are playback singers: Statement II: Director(x) -> FilmStar(x). Statement I: FilmStar(x) -> Singer(x). By hypothetical syllogism: Director(x) -> Singer(x). So All film directors are playback singers. Conclusion I FOLLOWS.
2. Check Conclusion II: Some film stars are film directors: Statement II says: All film directors are film stars. This means every element of the director set is also in the film star set. Since the director set is a non-empty subset of film stars, we can say: Some film stars are (specifically those who are) directors. Therefore 'Some film stars are film directors' FOLLOWS.
3. State the combined result: Both Conclusion I (transitivity of subset) and Conclusion II (particular from universal) follow from the given statements. Therefore option D is correct.