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 parrots are crows. All crows are eagles. Conclusions: I. All parrots are eagles. Il. Some crows are parrots.
Solving Statements and Conclusions Logic Puzzles
Let's break down this logical reasoning question involving statements and conclusions about parrots, crows, and eagles. We are given two statements that we must assume are true, and we need to determine which of the given conclusions logically follow from these statements.
Understanding the Statements
The statements provided are:
- All parrots are crows.
- All crows are eagles.
These statements establish relationships between three categories: parrots, crows, and eagles. The first statement tells us that the set of all parrots is entirely contained within the set of crows. The second statement tells us that the set of all crows is entirely contained within the set of eagles.
Using Venn Diagrams for Logical Reasoning
Venn diagrams are a helpful tool to visualize these kinds of relationships.
- Statement 1: "All parrots are crows" means the circle representing 'Parrots' should be completely inside the circle representing 'Crows'.
- Statement 2: "All crows are eagles" means the circle representing 'Crows' should be completely inside the circle representing 'Eagles'.
If we combine these two statements, we get a diagram where the 'Parrots' circle is inside the 'Crows' circle, and the 'Crows' circle is inside the 'Eagles' circle. This naturally places the 'Parrots' circle completely inside the 'Eagles' circle as well.
Analyzing the Conclusions
Now let's examine each conclusion based on our understanding and visualization from the statements.
Conclusion I: All parrots are eagles.
Based on our combined statements ("All parrots are crows" and "All crows are eagles"), we can see that if something is a parrot, it must first be a crow (from Statement 1), and if it is a crow, it must then be an eagle (from Statement 2). Therefore, anything that is a parrot must also be an eagle.
This conclusion logically follows from the given statements.
Conclusion II: Some crows are parrots.
Statement 1 says "All parrots are crows". This means that every single parrot is also a crow. If there are any parrots at all, then there must be some individuals that are both crows and parrots. The set of parrots is a subset of the set of crows.
The statement "All A are B" always implies that "Some B are A" (assuming there is at least one A). If all parrots are crows, then certainly some portion (at least the group of parrots) of the crows are parrots.
This conclusion logically follows from the given statements.
Determining Which Conclusions Follow
We have analyzed both conclusions:
- Conclusion I: All parrots are eagles. - Follows.
- Conclusion II: Some crows are parrots. - Follows.
Since both conclusions logically follow from the given statements, the correct option is the one stating that both conclusions I and II follow.
| Statement | Relationship | Visual |
|---|---|---|
| All parrots are crows. | Parrots ⊂ Crows | Parrots circle inside Crows circle. |
| All crows are eagles. | Crows ⊂ Eagles | Crows circle inside Eagles circle. |
| Conclusion | Analysis | Follows? |
|---|---|---|
| I. All parrots are eagles. | If Parrots ⊂ Crows and Crows ⊂ Eagles, then Parrots ⊂ Eagles. | Yes |
| II. Some crows are parrots. | If All Parrots are Crows, then the set of Parrots is a subset of Crows. This implies Some Crows are Parrots. | Yes |
Conclusion Summary
Based on our analysis, both Conclusion I ("All parrots are eagles") and Conclusion II ("Some crows are parrots") logically follow from the given statements.
Revision Table: Statements and Conclusions
| Concept | Explanation | Example (from question) |
|---|---|---|
| Statement | A premise assumed to be true for the purpose of the argument. | All parrots are crows. |
| Conclusion | A judgment or decision reached by reasoning from the statements. | All parrots are eagles. |
| Logical Inference | Deriving a conclusion that must be true if the statements are true. | From "All A are B" and "All B are C", we infer "All A are C". |
| 'All A are B' implies 'Some B are A' | If the entire set A is part of set B, then some members of B (those in A) are also in A. | 'All parrots are crows' implies 'Some crows are parrots'. |
Additional Information: Syllogisms and Logic
The type of logic problem discussed here is related to categorical syllogisms, which deal with statements about categories or classes of things. These statements often use quantifiers like "All", "Some", or "No".
- Categorical Statement Types:
- Universal Affirmative (A): All S are P.
- Universal Negative (E): No S are P.
- Particular Affirmative (I): Some S are P.
- Particular Negative (O): Some S are not P.
- Key Inferences: Understanding how these statement types relate to each other is crucial. For instance, a universal affirmative ("All A are B") implies a particular affirmative ("Some A are B") and also ("Some B are A", assuming A exists).
- Transitivity: As seen in this problem, the "All...are..." relationship is transitive. If A ⊂ B and B ⊂ C, then A ⊂ C.
Practicing with Venn diagrams or understanding the rules of inference for categorical logic helps in solving these statement and conclusion problems accurately.
Similar Questions
- In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. Some tables are chairs.
II. All desks are chairs.
III. No chair is a fan.
Conclusions:
I. Some desks are tables.
II. Some fans are desks. - In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. All tables are charts.
II. Some charts are graphs.
III. Some graphs are pies.
Conclusions:
I. No table is a graph.
II. Some pies are charts. - In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures. Three statements are given, followed by Two conclusions numbered I and II. Assuming the 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 statements.
Statements:
Some fractions are marts.
No mart is a stud.
All studs are frogs.
Conclusions:
I. Some fractions are definitely not studs.
II. Some fractions are definitely not marts.
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 calculators are lanterns.
Some lanterns are mobiles.
Conclusions:
I. All mobiles are calculators.
II. No mobile is a lantern.
III. Some mobiles are lanterns.
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 from the statements.
Statements:
No certificate is a paper.
All pens are papers.
Conclusions:
I. No certificate is a pen.
II. No paper is a certificate.
III. Some papers are pens.
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 officers are clerks.
All clerks are workers.
Conclusions:
I. Some workers are officers.
Il. No worker is an officer.
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 chargers are phones.
No phone is a watch.
Conclusions:
I. All phones are chargers.
Il. No charger is a watch.
Ill. No watch is a phone.
Two 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 wallets are bags.
Some bags are envelopes.
Conclusions:
I. Some wallets are envelopes.
II. No wallet is an envelope.
III. No bag is an envelope.Two 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 boys are brave.
All boys are punctual.
Conclusions:
I. Some brave are boys.
II. Some punctual are boys.
III. Some brave are punctual.
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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
