Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statement: 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.
Both conclusions I and II follow
Logical Reasoning Syllogism Analysis
This question tests your understanding of logical deduction, specifically using syllogisms. In syllogisms, we are given a set of statements (premises) and asked to determine which conclusions logically follow from those statements, assuming the statements are true. We can often use Venn diagrams or direct logical inference to solve such problems.
Statements Breakdown
Let's analyze the given statements:
- Statement I: All film stars are playback singers.
This statement implies that the set of "film stars" is entirely contained within the set of "playback singers."
Mathematically, we can represent this as: \(\text{Film Stars} \subset \text{Playback Singers}\) - Statement II: All film directors are film stars.
This statement implies that the set of "film directors" is entirely contained within the set of "film stars."
Mathematically, we can represent this as: \(\text{Film Directors} \subset \text{Film Stars}\)
Conclusions Evaluation
Now, let's examine each conclusion based on the statements:
Conclusion I: All film directors are playback singers.
To verify this conclusion, we combine the information from both statements:
- From Statement II, we know that all "film directors" are also "film stars."
- From Statement I, we know that all "film stars" are also "playback singers."
If every film director is a film star, and every film star is a playback singer, then it logically follows that every film director must also be a playback singer.
This can be visualized as a chain: Film Directors → Film Stars → Playback Singers.
So, \(\text{Film Directors} \subset \text{Film Stars}\) and \(\text{Film Stars} \subset \text{Playback Singers}\) implies \(\text{Film Directors} \subset \text{Playback Singers}\).
Therefore, Conclusion I logically follows from the given statements.
Conclusion II: Some film stars are film directors.
To verify this conclusion, let's look at Statement II:
- Statement II says: "All film directors are film stars."
If "All A are B" is true, it always implies that "Some B are A" is also true. For example, if all dogs are animals, then it is certainly true that some animals are dogs.
In our case, if "All film directors are film stars," then it must be true that "Some film stars are film directors." This is a direct inference from an "All" statement to a "Some" statement where the subject and predicate are swapped.
Therefore, Conclusion II logically follows from the given statements.
Final Syllogism Decision
Both Conclusion I ("All film directors are playback singers") and Conclusion II ("Some film stars are film directors") are logically derived from the given statements.
| Statement/Conclusion | Relationship | Logical Follows? |
|---|---|---|
| Statement I: All film stars are playback singers. | \(\text{Film Stars} \subset \text{Playback Singers}\) | (Premise) |
| Statement II: All film directors are film stars. | \(\text{Film Directors} \subset \text{Film Stars}\) | (Premise) |
| Conclusion I: All film directors are playback singers. | From \(\text{FD} \subset \text{FS}\) and \(\text{FS} \subset \text{PS} \implies \text{FD} \subset \text{PS}\) | Yes |
| Conclusion II: Some film stars are film directors. | From \(\text{All FD are FS} \implies \text{Some FS are FD}\) | Yes |
Based on our analysis, both conclusions I and II are valid deductions.
Important Questions from Instructions
All people in a certain are either ‘Knights’ or ‘Knaves’ and each person knows every other person’s identity. Knights NEVER lie, and knaves ALWAYS lie.
P says “Both of us are knights”, Q says “None of us are knaves”.
Which one of the following can be logically inferred from the above?Fact: If it rains, then the field is wet.
Read the following statements:
(i) It rains
(ii) The field is not wet
(iii) The field is wet
(iv) It did not rain
Which one of the options given below is NOT logically possible, based on the given fact?A smart city integrates all modes of transport, uses clean energy and promotes the sustainable use of resources. It also uses technology to ensure the safety and security of the city, something which critics argue, will lead to a surveillance state.
Which of the following can be logically inferred from the above paragraph?
(i) All smart cities encourage the formation of surveillance states.
(ii) Surveillance is an integral part of a smart city.
(iii) Sustainability and surveillance go hand in hand in a smart city.
(iv) There is a perception that smart cities promote surveillance.The binary operation □ is defined as a □ b = ab + (a + b), where a and b are any two real numbers. The value of the identity element of this operation, defined as the number x such that a □ x = a, for any a, is_______.
Social science disciplines were in existence in an amorphous form until the colonial period when they were intuitionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise of postcolonial countries like India, conventional ways of knowledge production have become obsolete.
Which of the following can be logically inferred from the above statements?
i) Social science disciplines have become obsolete.
ii) Social science disciplines had a pre – colonial origin
iii) Social science disciplines always promote colonialism
iv) Social science must maintain disciplinary boundaries.
