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 camels are bats. No bat is a parrot. Some camels are lions. Conclusions: I. Some bats are lions. II. No parrot is a camel. III. No parrot is a lion.
Both conclusions I and II follow
Syllogism Statements and Conclusions Analysis
This question requires us to analyze the given statements and determine which of the provided conclusions logically follow based on the rules of deductive reasoning, specifically syllogism.
Understanding the Statements
Let's break down the given statements:
- Statement 1: All camels are bats. (All C are B)
- Statement 2: No bat is a parrot. (No B is P)
- Statement 3: Some camels are lions. (Some C are L)
We assume these statements are true, regardless of whether they align with real-world facts.
Analyzing the Conclusions
We need to evaluate each conclusion based on the statements:
- Conclusion I: Some bats are lions. (Some B are L)
- Conclusion II: No parrot is a camel. (No P is C)
- Conclusion III: No parrot is a lion. (No P is L)
Logical Deduction Process
Let's examine each conclusion carefully:
Conclusion I: Some bats are lions.
Consider Statement 3: Some camels are lions. This means there is an overlap between the set of camels and the set of lions. Some members belong to both sets.
Now consider Statement 1: All camels are bats. This means every member of the set of camels is also a member of the set of bats.
If some camels are lions (Statement 3), and all camels are bats (Statement 1), then the camels that are also lions must necessarily be bats. This establishes an overlap between the set of bats and the set of lions.
Therefore, it logically follows that some bats are lions.
Conclusion I follows.
Conclusion II: No parrot is a camel.
Consider Statement 2: No bat is a parrot. This means there is absolutely no overlap between the set of bats and the set of parrots. They are mutually exclusive sets.
Now consider Statement 1: All camels are bats. This means the set of camels is entirely contained within the set of bats. If something is a camel, it must also be a bat.
Since the set of camels is inside the set of bats (Statement 1), and the set of bats has no members in common with the set of parrots (Statement 2), it follows that the set of camels can also have no members in common with the set of parrots.
Therefore, it logically follows that no camel is a parrot, which is equivalent to saying no parrot is a camel.
Conclusion II follows.
Conclusion III: No parrot is a lion.
We know from Statement 2 that No bat is a parrot.
From our analysis for Conclusion I, we deduced that Some bats are lions (Some B are L). This comes from 'Some C are L' and 'All C are B'.
So we have the relationship: Some lions are bats, and No bats are parrots.
This structure is "Some L are B" and "No B is P". This combination (I + E type statements) validly leads to an O-type conclusion: "Some L are not P".
The conclusion "Some lions are not parrots" tells us there is at least one lion that is not a parrot. It does NOT tell us that *no* parrot is a lion. There might still be some lions (those that are not bats, if any exist) that *are* parrots. The statements do not provide information to exclude this possibility.
Therefore, the conclusion "No parrot is a lion" does not logically follow from the given statements.
Conclusion III does not follow.
Summary of Conclusions
Based on our analysis:
- Conclusion I: Some bats are lions. (Follows)
- Conclusion II: No parrot is a camel. (Follows)
- Conclusion III: No parrot is a lion. (Does not follow)
Thus, both conclusions I and II follow from the given statements.
Revision Table: Syllogism Rules
| Statement Type | Symbolic Representation | Relationship |
|---|---|---|
| All A are B | A ⊂ B | Set A is entirely within Set B |
| No A is B | A ∩ B = ∅ | Sets A and B are mutually exclusive |
| Some A are B | A ∩ B ≠ ∅ | Sets A and B have at least one member in common |
| Some A are not B | Exists x such that x ∈ A and x ∉ B | At least one member of Set A is not in Set B |
Additional Information: Deductive vs Inductive Reasoning
This question uses deductive reasoning, which is common in syllogism problems. Deductive reasoning starts with general statements (premises) and arrives at a specific conclusion that is guaranteed to be true if the premises are true.
In contrast, inductive reasoning moves from specific observations to a general conclusion. Inductive conclusions are probable but not guaranteed to be true, even if the observations are correct.
Syllogism problems always rely on the strict rules of deductive logic. The conclusions must follow necessarily from the statements provided, irrespective of outside information.
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.
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Some cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
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III. Some cards are copies.
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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.
