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. Statement 1 : All shells are skins. Statement 2 : No skins are cats. Conclusion I : No shells are cats. Conclusion II : Some skins are shells.
Both I and II follow
Logical Reasoning: Statements & Conclusions Analysis
This solution analyzes logical statements about shells, skins, and cats to determine the validity of given conclusions.
Analyzing the Statements
Statement 1: All shells are skins.
- This implies the set 'shells' is a subset of the set 'skins'.
Statement 2: No skins are cats.
- This implies the sets 'skins' and 'cats' are disjoint.
Evaluating Conclusion I: No shells are cats
Reasoning:
- Since all 'shells' are within the 'skins' set (Statement 1), and the 'skins' set is entirely separate from the 'cats' set (Statement 2), it must be true that 'shells' are also separate from 'cats'.
- Therefore, Conclusion I logically follows.
Evaluating Conclusion II: Some skins are shells
Reasoning:
- Statement 1, "All shells are skins," directly means that any existing shell is necessarily a skin.
- This establishes that the 'skins' category includes the 'shells' category.
- Therefore, it is true that at least some skins are shells. Conclusion II logically follows.
Overall Findings
Both Conclusion I and Conclusion II are valid deductions based on the provided statements.
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.
