Select the option that is true about the Statements and Conclusions given: Statements: All roses are flowers All lilies are flowers Conclusions: I. All roses are lilies II. All lilies are roses
None of the conclusion I or II follows
Understanding Statements and Conclusions in Logic
This question asks us to analyze the relationship between given statements and determine which conclusions logically follow from them. This is a common type of problem in logical reasoning, often involving categories and relationships between them.
Analyzing the Statements
We are given two statements:
- Statement 1: All roses are flowers
- Statement 2: All lilies are flowers
Let's think about what these statements tell us. Statement 1 means that the set of "roses" is completely contained within the set of "flowers". Statement 2 means that the set of "lilies" is also completely contained within the set of "flowers".
Imagine the set of all flowers as a large circle. Both the set of roses and the set of lilies are smaller circles *inside* this large circle of flowers. The statements tell us they are both flowers, but they don't tell us anything definite about the relationship *between* roses and lilies.
Analyzing the Conclusions
We need to evaluate two conclusions:
- Conclusion I: All roses are lilies
- Conclusion II: All lilies are roses
Checking the Validity of Conclusion I
Conclusion I states that all roses are lilies. Based on our statements, we know all roses are flowers and all lilies are flowers. However, this doesn't necessarily mean that roses are a type of lily or that the set of roses is contained within the set of lilies. Roses and lilies could be two distinct types of flowers. For example, if we consider the set of 'Fruits', and 'Apples are Fruits' and 'Bananas are Fruits', it doesn't mean 'All Apples are Bananas'. Therefore, the conclusion "All roses are lilies" does not logically follow from the given statements.
Checking the Validity of Conclusion II
Conclusion II states that all lilies are roses. Similarly, from the statements that all lilies are flowers and all roses are flowers, we cannot conclude that lilies are a type of rose or that the set of lilies is contained within the set of roses. Lilies and roses are simply stated to be two different groups, both belonging to the larger group of flowers. Just as with the apple and banana example, knowing both are fruits doesn't make all bananas apples. Thus, the conclusion "All lilies are roses" does not logically follow from the given statements.
Determining Which Conclusions Follow
Since neither Conclusion I (All roses are lilies) nor Conclusion II (All lilies are roses) can be definitively proven true based *only* on the information provided in the statements, neither conclusion logically follows.
Therefore, the correct answer is that none of the conclusions I or II 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.
