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
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2015
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.