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
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 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.
