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
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.
