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 bats are birds. Some rats are bats. Conclusions: I. Some rats are birds. II. Some birds are bats. III. All rats are bats.
Analyzing Syllogism Statements and Conclusions
This question asks us to analyze a set of statements and determine which of the given conclusions logically follow from them. This is a classic syllogism problem where we assume the statements are true, regardless of real-world facts, and use deductive reasoning to check the conclusions.
Understanding the Syllogism Statements
We are given two statements:
- Statement 1: All bats are birds.
- Statement 2: Some rats are bats.
Let's interpret these statements:
- Statement 1 is a universal affirmative statement. It means that the entire category of 'bats' is included within the category of 'birds'. If something is a bat, it must also be a bird.
- Statement 2 is a particular affirmative statement. It means that there is at least one rat that belongs to the category of 'bats'. However, it does not tell us anything about 'all' rats.
Evaluating the Conclusions
Now, let's examine each conclusion based on the truth of the statements.
Conclusion I: Some rats are birds.
We know from Statement 2 that there are some rats that are bats. We also know from Statement 1 that all bats are birds. Therefore, the 'some rats' that are also 'bats' must necessarily also be 'birds'. This conclusion logically follows from the given statements.
Conclusion II: Some birds are bats.
Statement 1 says "All bats are birds". This means the set of bats is a subset of the set of birds. If all members of set A are members of set B, then it logically follows that some members of set B are members of set A (specifically, all the members of set A are among those 'some' members of set B). Thus, if all bats are birds, then some birds must be bats. This conclusion logically follows.
Conclusion III: All rats are bats.
Statement 2 tells us "Some rats are bats". This only guarantees that there is at least one rat that is a bat. It does not provide any information to suggest that *all* rats are bats. It's possible that only a small portion of rats are bats, and the rest are not. Therefore, this conclusion does not logically follow from the given statements.
Summary of Conclusions
Based on our analysis, Conclusions I and II logically follow from the statements, while Conclusion III does not.
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| I. Some rats are birds. | Yes | Some rats are bats (Stmt 2), and all bats are birds (Stmt 1). Therefore, some rats are birds. |
| II. Some birds are bats. | Yes | All bats are birds (Stmt 1). If all of A are B, then some of B are A. |
| III. All rats are bats. | No | Only "Some rats are bats" is given (Stmt 2). This does not imply "All rats are bats". |
Therefore, only conclusions I and II follow.
Revision Table: Syllogism Logic
Here's a quick overview of the concepts involved in this syllogism problem:
- Statements: The given premises assumed to be true.
- Conclusions: The inferences drawn from the statements.
- Logically Follows: A conclusion follows if it must be true whenever the statements are true.
- Universal Affirmative (All A are B): Means set A is entirely contained within set B.
- Particular Affirmative (Some A are B): Means there is at least one element common to both sets A and B.
Additional Information: Syllogism Types
Syllogisms are a fundamental part of deductive reasoning. They typically consist of two premises (statements) and a conclusion. The statements relate two terms with a third term, and the conclusion relates the two terms. In this problem:
- Term 1: Rats
- Term 2: Birds
- Middle Term: Bats
The statements establish relationships between Rats and Bats, and Bats and Birds. The valid conclusions are those that necessarily hold true for the relationship between Rats and Birds based on these established links.
Similar Questions
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.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some Z are X.
II. Some W are Z.
Conclusions:
I. Some X are not W.
II. Some X are not Z.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some mobiles are flat.
All flats are TVs.
Some TVs are plastic.
Conclusions:
I. Some mobiles are TVs.
II. Some flats are plastic.
III. All plastic are TVs.
Three statements are given, followed by three conclusions numbered I, II and III.Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
No cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. No A is B.
II. No C is B.
Conclusion:
I. Some C are not A.
II. Some A are B.
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 benches are tables.
Some tables are chairs.
Some chairs are pencils.
Conclusions:
I. Some benches are chairs.
II. Some tables are pencils.
III. Some pencils are chairs.
IV. Some pencils are tables.
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.
