Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the
conclusions and then decide which of the given conclusion(s) logically follows the given statements.
Statements:
I. Some T are S.
II. No R is S.
Conclusions:
I. No S is R.
II. No R is T.
III. No S is T.
Logical Deduction from Statements
This section explains how to determine which conclusions logically follow from the given statements.
Statements Analysis
- Statement I: Some T are S. (This indicates an overlap between the set T and the set S).
- Statement II: No R is S. (This indicates that the set R and the set S are completely separate; they have no common elements).
Conclusions Evaluation
-
Conclusion I: No S is R.
Statement II states "No R is S". This assertion is logically equivalent to "No S is R". Therefore, Conclusion I directly and logically follows from Statement II.
-
Conclusion II: No R is T.
Statement I ("Some T are S") implies that some elements belong to both T and S, while others might belong only to T. Statement II ("No R is S") means R and S are distinct. While the elements that are both T and S cannot be R, Statement I does not provide information about the elements of T that are *not* S. These elements could potentially be R. Thus, we cannot conclude with certainty that "No R is T".
-
Conclusion III: No S is T.
Statement I explicitly states "Some T are S". This directly implies that there is at least one element common to both T and S, meaning "Some S are T" is true. This contradicts the conclusion "No S is T". Therefore, Conclusion III does not follow.
Result
Based on the logical analysis of the statements, only Conclusion I ("No S is R") necessarily 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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
