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.
Either conclusion I or II follows
Statements and Conclusions Analysis
This section analyzes the logical implications of the provided statements concerning sets Strong, Animals, Tigers, and Sharp.
- Statement 1: All Strong are animals. This means the set of Strong entities is entirely contained within the set of Animals. Mathematically, $ \text{Strong} \subseteq \text{Animals} $.
- Statement 2: Some animals are Tigers. This implies there is at least one entity that is both an Animal and a Tiger. Mathematically, $ \text{Animals} \cap \text{Tigers} \neq \emptyset $.
- Statement 3: All Tigers are Sharp. This means the set of Tigers is entirely contained within the set of Sharp entities. Mathematically, $ \text{Tigers} \subseteq \text{Sharp} $.
Logical Deduction
- Combining Statement 2 and Statement 3: Since some Animals are Tigers ($ \text{Animals} \cap \text{Tigers} \neq \emptyset $) and all Tigers are Sharp ($ \text{Tigers} \subseteq \text{Sharp} $), it logically follows that there must be some Animals that are also Sharp ($ \text{Animals} \cap \text{Sharp} \neq \emptyset $).
- Now, consider the relationship between Strong and Sharp. We know from Statement 1 that $ \text{Strong} \subseteq \text{Animals} $. We also know that there's a non-empty intersection between Animals and Sharp ($ \text{Animals} \cap \text{Sharp} \neq \emptyset $).
- The critical point is whether the subset 'Strong' (which resides within 'Animals') overlaps with the 'Sharp' set.
- Scenario A: The 'Strong' entities within 'Animals' might overlap with the 'Sharp' entities within 'Animals'. If this overlap occurs, then Conclusion I (Some Strong are Sharp) would be true.
- Scenario B: The 'Strong' entities within 'Animals' might be entirely separate from the 'Sharp' entities within 'Animals'. If they are separate, then Conclusion II (No Strong is Sharp) would be true.
- The given statements do not provide enough information to determine whether Scenario A or Scenario B is the actual situation. However, these two scenarios are mutually exclusive and cover the possibilities concerning the relationship between Strong and Sharp given the premises.
Final Conclusion
Because the statements allow for two possibilities—either some Strong are Sharp (Conclusion I) or no Strong is Sharp (Conclusion II)—and these two conclusions are contradictory, it must be the case that one of them is true. Therefore, Either conclusion I or II follows.
Similar Questions
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 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.
