Premises: All film stars are playback singers. All film directors are

Premises: All film stars are playback singers. All film directors are film stars.
Conclusions:

I. All film directors are playback singers.
II. Some film stars are film directors.

Which of the following conclusions follow logically?

Only I

Only II

Both I and II

Neither I nor II

This question was previously asked in

UPSC CAPF – 2015

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Both Conclusion I and Conclusion II follow logically from the given premises.

Premise 1: All film stars are playback singers. (FS ⊆ PS)
Premise 2: All film directors are film stars. (FD ⊆ FS)
Conclusion I: All film directors are playback singers.
From Premise 2, the set of film directors (FD) is a subset of the set of film stars (FS). From Premise 1, the set of film stars (FS) is a subset of the set of playback singers (PS). If A ⊆ B and B ⊆ C, then A ⊆ C. Therefore, FD ⊆ PS. This means all film directors are playback singers. Conclusion I is true.
Conclusion II: Some film stars are film directors.
Premise 2 states that all film directors are film stars (FD ⊆ FS). This is a universal affirmative statement (‘All A are B’). In traditional logic, a universal affirmative statement ‘All A are B’ implies the particular affirmative statement ‘Some B are A’, provided that the set A is not empty. Assuming there is at least one film director (which is standard in such problems unless specified otherwise), then there is at least one member in the set FD. Since every member of FD is also in FS, there must be at least one member in FS that is also in FD. Thus, some film stars are film directors. Conclusion II is true.

This problem demonstrates the transitivity of the subset relationship (for Conclusion I) and the conversion of a universal affirmative statement (for Conclusion II, assuming existential import). If we strictly adhere to modern formal logic without existential import for universal statements, ‘All A are B’ does not necessarily imply ‘Some B are A’ if the set A is empty. However, in typical syllogism questions, especially in the context of competitive exams like UPSC, the assumption of existential import for the subject class of universal statements is generally followed unless explicitly negated. Therefore, ‘All film directors are film stars’ implies ‘Some film stars are film directors’ as long as there exists at least one film director.

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