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
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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.
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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".
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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
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
