GATE EC 2015 Set 2 — Question 7
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
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.
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.
Correct answer
(D) Both conclusions I and II follow.
Solution
Let be the set of film directors, be the set of film stars, and be the set of playback singers.
From the statements:
Conclusion II: "Some film stars are film directors" means . Since , any element in is also in . Assuming the set of film directors is non-empty, there are elements in that are also in . Thus, some film stars are film directors. This is true.Therefore, both conclusions I and II follow.
From the statements:
1. (All film stars are playback singers)
2. (All film directors are film stars)
Combining these, we get .Conclusion I: "All film directors are playback singers" means . This is true since and .Conclusion II: "Some film stars are film directors" means . Since , any element in is also in . Assuming the set of film directors is non-empty, there are elements in that are also in . Thus, some film stars are film directors. This is true.Therefore, both conclusions I and II follow.
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