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 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.
