Read the given statements and conclusions carefully. Assuming that 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 follow(s) from the statements. Statements: Some actors are choreographers. All choreographers are producers. Not a single producer is a director. Conclusions: I. Some actors are directors. II. Not a single actor is a director.
Either conclusion I or II follows
To determine which conclusion follows, let's map out the relationships between the groups.
Analysis of Statements
Some actors are choreographers: There is an intersection between the "Actors" circle and the "Choreographers" circle.
All choreographers are producers: The entire "Choreographers" circle is contained within the "Producers" circle. This means the part of "Actors" that overlapped with "Choreographers" is now also part of "Producers."
Not a single producer is a director: The "Producers" circle and the "Directors" circle are completely separate (disjoint sets).
Evaluating the Conclusions
The relationship between Actors and Directors is the core of both conclusions. From our statements, we know:
Some Actors are Producers (the ones who are also Choreographers).
No Producer is a Director.
Therefore, we can certain that some actors (the ones who are producers) are definitely not directors.
However, for the remaining actors who are not producers, we have no information. They could be directors, or they might not be.
Conclusion I: Some actors are directors. This is a possibility, but it is not a certainty. Therefore, it does not logically follow.
Conclusion II: Not a single actor is a director. This is also a possibility, but not a certainty (since some actors outside the producer circle could be directors). Therefore, it does not logically follow.
The "Either-Or" Case
In syllogisms, an Either-Or relationship occurs when:
Both conclusions are independently "False" or "Possible but not certain."
They form a Complementary Pair (e.g., "Some A are B" and "No A is B").
They have the same Subject and Predicate.
Since Conclusion I is a "Some" statement and Conclusion II is a "No" statement involving the same two groups (Actors and Directors), they are mutually exclusive and cover all possibilities. Either there is at least one actor who is a director, or there isn't a single one.
The correct choice is Option 1: Either conclusion I or II follows.
Important Questions from Syllogism
Read the given statements and conclusions carefully. Assuming that 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 follow(s) from the statements.
Statements:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
Read the given statements and conclusions carefully. Assuming that 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 follow(s) from the statements.
Statements:
All directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
Read the given statements and conclusions carefully. Assuming that 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 lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
Read the given statements and conclusions carefully. Assuming that 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 follow(s) from the statements.
Statements:
Some cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
Read the given statements and conclusions carefully. Assuming that 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 follow(s) from the statements.
Statements:
All employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
