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 squirrels are lizards. All lizards are goose. Conclusions: I. Some squirrels are not goose. II. Some lizards are squirrels.
Conclusions II and III follow
Solving Syllogism Problems: Squirrels, Lizards, and Goose
Syllogism questions test your ability to draw logical conclusions from given statements, assuming the statements are true regardless of common knowledge. We will analyze the statements and conclusions provided in this problem.
Understanding the Syllogism Statements
The statements given are:
- All squirrels are lizards.
- All lizards are goose.
These statements establish relationships between three categories: Squirrels, Lizards, and Goose. 'All A are B' means that the category A is entirely contained within the category B.
Visualizing the Statements with Venn Diagrams
We can represent these relationships using Venn diagrams:
- Statement 1: "All squirrels are lizards." This means the circle representing Squirrels is inside the circle representing Lizards.
- Statement 2: "All lizards are goose." This means the circle representing Lizards is inside the circle representing Goose.
Combining these, if Squirrels are inside Lizards, and Lizards are inside Goose, then Squirrels must also be inside Goose. The diagram shows a set for Squirrels nested within Lizards, which is nested within Goose.
Analyzing the Syllogism Conclusions
Now let's evaluate each conclusion based on our understanding and visualization of the statements:
Conclusion I: Some squirrels are not goose.
From the statements "All squirrels are lizards" and "All lizards are goose," we logically deduce that "All squirrels are goose." If all squirrels are goose, it is impossible for any squirrel (and therefore 'some' squirrels) to not be a goose. Thus, this conclusion does not follow from the statements.
Conclusion II: Some lizards are squirrels.
Statement 1 says, "All squirrels are lizards." If all members of the Squirrels category are also in the Lizards category, then the Lizards category must contain all the Squirrels. This means that at least some members of the Lizards category are squirrels (specifically, all the members that are squirrels). The phrase 'Some A are B' is logically implied by 'All B are A' (assuming B is not an empty set, which is standard in these problems).
Therefore, Conclusion II logically follows from Statement 1.
Conclusion III: Some goose are squirrels.
We deduced that "All squirrels are goose." If all members of the Squirrels category are also in the Goose category, then the Goose category must contain all the Squirrels. This means that at least some members of the Goose category are squirrels. Similar to the previous conclusion, 'Some A are B' is logically implied by 'All B are A'.
Therefore, Conclusion III logically follows from the combined statements.
Summary of Conclusions
- Conclusion I: Some squirrels are not goose. (Does NOT follow)
- Conclusion II: Some lizards are squirrels. (FOLLOWS)
- Conclusion III: Some goose are squirrels. (FOLLOWS)
Based on the analysis, conclusions II and III logically follow from the given statements.
| Statement/Conclusion | Analysis | Follows? |
|---|---|---|
| Statement 1: All squirrels are lizards. | Squirrels <figure> </figure> Lizards | - |
| Statement 2: All lizards are goose. | Lizards <figure> </figure> Goose | - |
| Deduction: All squirrels are goose. | Squirrels <figure> </figure> Goose | - |
| Conclusion I: Some squirrels are not goose. | Contradicts "All squirrels are goose". | No |
| Conclusion II: Some lizards are squirrels. | Implied by "All squirrels are lizards". | Yes |
| Conclusion III: Some goose are squirrels. | Implied by "All squirrels are goose". | Yes |
Revision Table: Key Syllogism Rules
| Statement Type | Logical Implication (Conversion) |
|---|---|
| All A are B | Some B are A |
| No A are B | No B are A |
| Some A are B | Some B are A |
| Some A are not B | No direct standard conversion |
Additional Information on Syllogisms
Syllogisms are a form of deductive reasoning where a conclusion is drawn from two given or assumed propositions (premises). There are different types of statements in syllogisms:
- Universal Affirmative: All A are B (e.g., All squirrels are lizards)
- Universal Negative: No A are B (e.g., No squirrels are birds)
- Particular Affirmative: Some A are B (e.g., Some lizards are green)
- Particular Negative: Some A are not B (e.g., Some goose are not white)
In this problem, we dealt with universal affirmative statements. A key principle used here is the implication that 'All A are B' means 'Some B are A'. This is a valid inference unless A represents an empty set, which is usually not the case in these logical reasoning puzzles.
Similar Questions
- Read the following statement carefully and identify the conclusion that follows.
Statement:
All poets are writers. Some writers are critics. No critic is a fool.
Conclusions:
I. Some poets are critics.
II. Some writers are not fools. - Statements: All dancers are artists. No artist is lazy.
Conclusions: I. No dancer is lazy. II. Some lazy are dancers. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All oranges are fruits. No fruit is a vegetable. All vegetables are green.
Conclusions:
I. No orange is green.
II. No orange is a vegetable. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All kids are students. Some students are athletes. No athlete is a scholar.
Conclusions:
I. Some kids may be athletes.
II. No kid is a scholar. - Statements: Some keys are locks. Some locks are doors.
Conclusions: I. Some keys are doors. II. All locks being keys is a possibility. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All musicians are artists. Some artists are dancers. No dancer is blind.
Conclusions:
I. Some artists are not blind.
II. All blind are not dancers. Statements: Some pens are papers. All papers are books. Conclusions: I. Some pens are books. II. All books are pens.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All birds are animals. Some animals are tigers. No tiger is a bird.
Conclusions:
I. Some tigers are birds.
II. Some animals are not birds.
- Statements: All dogs are cats. Some cats are rats. Conclusions: I. Some rats are dogs. II. All dogs are rats.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All pens are blue things. Some blue things are plastic. No plastic is recyclable.
Conclusions:
I. Some pens are plastic.
II. Some blue things are not recyclable.
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.
