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.
Only conclusion III follows
Logical Reasoning: Analyzing Syllogism Statements and Conclusions
This question tests your ability to draw logical conclusions from given statements, a fundamental part of logical reasoning and syllogisms. We are given three statements involving the relationships between different categories: benches, tables, chairs, and pencils. All the statements use the quantifier "Some", indicating a partial relationship.
Understanding the Statements
The given statements are:
- Some benches are tables. (Relationship between benches and tables)
- Some tables are chairs. (Relationship between tables and chairs)
- Some chairs are pencils. (Relationship between chairs and pencils)
In logical terms, "Some A are B" means that there is at least one element that belongs to both category A and category B. It does not imply that all A are B, or that all B are A, or even that most A are B. It just confirms the existence of a non-empty intersection between the two sets.
Evaluating the Conclusions
Let's examine each conclusion to see if it logically follows from the statements:
Conclusion I: Some benches are chairs.
We have statements connecting benches to tables (Some benches are tables) and tables to chairs (Some tables are chairs). The relationship is B <--Some--> T <--Some--> C. While benches and chairs are linked through tables, the "Some" quantifier in both connections does not guarantee a direct "Some" relationship between benches and chairs. It's possible to draw scenarios (using Venn diagrams, for instance) where benches and chairs have no overlap, even though they both overlap with tables. Therefore, this conclusion does not logically follow.
Conclusion II: Some tables are pencils.
We have statements connecting tables to chairs (Some tables are chairs) and chairs to pencils (Some chairs are pencils). The relationship is T <--Some--> C <--Some--> P. Similar to Conclusion I, a chain of "Some" relationships across three terms (tables, chairs, pencils) does not guarantee a direct "Some" relationship between the first and the third term (tables and pencils). There might be scenarios where tables and pencils do not overlap despite both overlapping with chairs. Therefore, this conclusion does not logically follow.
Conclusion III: Some pencils are chairs.
The third statement is "Some chairs are pencils". Conclusion III is "Some pencils are chairs". In logic, the statement "Some A are B" is equivalent to "Some B are A". This is known as the simple conversion of an 'I' statement (Particular Affirmative). Since "Some chairs are pencils" is given as true, its simple conversion "Some pencils are chairs" must also be true. Therefore, this conclusion logically follows from the third statement.
Conclusion IV: Some pencils are tables.
This conclusion proposes a relationship between pencils and tables (P <--Some--> T). The statements provide relationships P <--Some--> C and C <--Some--> T. This is the same structural issue as Conclusion II (and I), just with the terms in a different order. A chain of "Some" relationships between P, C, and T does not guarantee a direct "Some" relationship between P and T. Therefore, this conclusion does not logically follow.
Summary of Conclusions
- Conclusion I (Some benches are chairs): Does not follow.
- Conclusion II (Some tables are pencils): Does not follow.
- Conclusion III (Some pencils are chairs): Follows.
- Conclusion IV (Some pencils are tables): Does not follow.
Based on the analysis, only Conclusion III logically follows from the given statements.
Revision Table: Syllogism Rules for 'Some'
Here's a quick look at how 'Some' statements behave in basic syllogisms:
| Statement Type | Conversion Rule | Combining with another 'Some' statement |
|---|---|---|
| Some A are B | Converts to "Some B are A". This is always valid. | Two 'Some' statements (e.g., Some A are B, Some B are C) yield no definite conclusion about the relationship between A and C. |
Additional Information on Logical Reasoning and Syllogisms
Logical reasoning questions involving statements and conclusions often use syllogisms. A syllogism is a type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
- Components: Syllogisms typically have two statements (premises) and one conclusion. However, exam questions can involve more statements.
- Quantifiers: Common quantifiers are "All", "No", "Some", and "Some not". The rules for drawing conclusions depend heavily on the quantifiers used.
- Venn Diagrams: A popular method to solve syllogism problems is by using Venn diagrams. You draw circles representing the categories and shade or mark the areas based on the statements. If a conclusion is true in ALL possible diagrams drawn from the statements, then it logically follows.
- Rules of Inference: There are formal rules in logic (like the conversion rule used above) that dictate which conclusions can be drawn from premises.
In problems with multiple 'Some' statements linking several categories, be cautious. 'Some' links in a chain (A-B-C) do not automatically create a 'Some' link between the ends (A-C).
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.
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 tyre are white.
II. All grey are white.
Conclusions:
I. No white is tyre.
II. No tyre is grey.
III. Some white are not grey.
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.
