The next three (03) items have two premises and two conclusions. If the premises are assumed to be true (irrespective of factuality), then, in respect
of each of the items given below, which of the following conclusions follow logically?
Premises : All film stars are playback singers. All film directors are film stars.
Conclusion: I. All film directors are playback singers.
II. Some film stars are film directors.
Premises Analysis
- Premise 1: All film stars are playback singers. This means if someone is a film star, they are definitely a playback singer. (Formal representation: $\forall x (\text{FilmStar}(x) \implies \text{PlaybackSinger}(x))$)
- Premise 2: All film directors are film stars. This means if someone is a film director, they are definitely a film star. (Formal representation: $\forall x (\text{FilmDirector}(x) \implies \text{FilmStar}(x))$)
Conclusion I Verification
The conclusion is: All film directors are playback singers.
- Based on Premise 2, every film director is a film star.
- Based on Premise 1, every film star is a playback singer.
- By combining these, we can deduce that if someone is a film director, they must be a film star, and consequently, they must also be a playback singer. This is a form of logical transitivity.
- Formal deduction: $\forall x (\text{FilmDirector}(x) \implies \text{FilmStar}(x)) \land \forall x (\text{FilmStar}(x) \implies \text{PlaybackSinger}(x)) \implies \forall x (\text{FilmDirector}(x) \implies \text{PlaybackSinger}(x))$.
- Therefore, Conclusion I is valid.
Conclusion II Verification
The conclusion is: Some film stars are film directors.
- Premise 2 states "All film directors are film stars." This means the group of film directors is entirely contained within the group of film stars.
- Assuming that the category "film directors" is not empty (i.e., there exists at least one film director), then this individual must also be a film star.
- This implies that there exist individuals who belong to both the category of film stars and the category of film directors.
- Formal interpretation: If $\exists x (\text{FilmDirector}(x))$, then from Premise 2, $\exists x (\text{FilmDirector}(x) \land \text{FilmStar}(x))$. This supports "Some film stars are film directors."
- Therefore, Conclusion II is valid.
Final Verdict
Since both Conclusion I and Conclusion II logically follow from the given premises, the correct option is that both conclusions are valid.
Important Questions from Conventional Syllogism
- Consider the following Statements and Conclusions :
Statements : Mohan is a good sportsman.
Sportsmen are healthy.
Conclusions : I. All healthy persons are sportsmen.
II. Mohan is healthy.
Which one of the following is correct? Premises : All metals are grey in colour. Some metals are heavy.
Conclusion: I. All heavy metals are grey in colour.
II. All light metals are not grey in colour.Premises : All apples are golden in colour. No golden coloured things are cheap.
Conclusion: I. All apples are cheap.
II. Golden coloured apples are not cheap.Read the given statement and conclusions carefully. Assuming that the information given in the statement is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statement.
Statement:
All reds are black.
Conclusions:
1. Some blacks are red.
2. Some reds are black.
Read the given statements and conclusions carefully. Assuming the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follows from the statements.
Statements:
All benches are bags.
Some bags are pillows.
Some bags are not chairs.
Conclusions:
Some benches are pillows.
Some pillows are chairs.
