GATE2015 EC-2: GA- 7

Question

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.

Statements:

1. All film stars are playback singers.
2. All film directors are film stars.

Conclusions:

1. All film directors are playback singers.
2. 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.

Comments

Please change the selected answer. The answer is option d).

Answer 1

1. All film directors are film stars
2. All film stars are playback singers.

$A \implies B$ and $B \implies C$ means $A \implies C.$ So All film directors are playback singers.

Conclusion 2 is also true as even if one film director exist, he must be a film star. (We have to assume domain sets to be non-empty here)

Correct Answer: Option D

Comments

answer should be option D , please correct it.

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Can someone explain conclusion2

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But as per proposition logic we can say A→ B but not Some B→ A. Bit confused at that part

Answer 2

Both the conclusions follow. You can verify it by drawing venn diagram representation.

Option D

Comments

@Sreyas S

Please tell the method of how to draw venn diagrams for solving such problems

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yeah is it possible??