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.
Only I and II follow
Logical Reasoning: Statements and Conclusions
This question requires analyzing logical connections between given statements and conclusions. We need to determine which conclusions are necessarily true based only on the provided statements.
Evaluating Conclusion I: Some forty are thirty.
Statement: "All thirty are forty."
Reasoning: If every member of the 'thirty' group is also a member of the 'forty' group, it logically follows that at least some members of the 'forty' group are indeed 'thirty'. This is a standard conversion of an "All A are B" statement to "Some B are A", assuming that the categories are not empty.
Result: Conclusion I logically follows.
Evaluating Conclusion II: Some seventy are sixty.
Statement: "All sixty are seventy."
Reasoning: Similar to the analysis for Conclusion I, if every 'sixty' is a 'seventy', then it must be true that some 'seventy' are 'sixty'.
Result: Conclusion II logically follows.
Evaluating Conclusion III: No thirty is twenty.
Statement: "All twenty are thirty."
Reasoning: The statement "All twenty are thirty" means that the set of 'twenty' is entirely contained within the set of 'thirty'. This directly implies that any individual identified as 'twenty' must also be 'thirty'. Consequently, it is impossible for 'no thirty to be twenty'; in fact, some thirty *must* be twenty. Therefore, this conclusion contradicts the given statement.
Result: Conclusion III does not follow.
Final Decision
Based on the analysis, only conclusions I and II are logically and definitely derived from the given statements.
Therefore, the correct option is the one stating that only I and II follow.
Similar Questions
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.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:
1. Some players are singers.
2. All singers are tall.
3. Some players are strong.
Conclusions:
I. Some players are tall.
II. All players are strong.
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.
