Three Statements are given followed by Four conclusions numbered I, II, III and IV. 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 copies are pillows. Some pillows are laptops. Some laptops are pens. Conclusions: I. Some copies are laptops. II. Some pillows are pens. III. Some pens are laptops. IV. Some pens are pillows.
Only conclusion III follows.
Understanding Syllogism Statements and Conclusions
This question asks us to analyze a set of statements and determine which of the given conclusions logically follow from them, based on the rules of syllogism. We are given three statements involving the categories Copies, Pillows, Laptops, and Pens.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: Some copies are pillows. (C → P, where → indicates 'some')
- Statement 2: Some pillows are laptops. (P → L)
- Statement 3: Some laptops are pens. (L → S, using S for Pens to avoid confusion with P for Pillows)
These are all 'I' type propositions (Some A are B), indicating a partial overlap between the categories mentioned in each statement.
Analyzing the Conclusions
Now let's look at the conclusions we need to test:
- Conclusion I: Some copies are laptops. (C → L)
- Conclusion II: Some pillows are pens. (P → S)
- Conclusion III: Some pens are laptops. (S → L)
- Conclusion IV: Some pens are pillows. (S → P)
Evaluating Each Conclusion
We need to see if these conclusions can be definitively derived from the given statements. We can use methods like Venn diagrams or the rules of syllogism to evaluate.
Evaluating Conclusion I: Some copies are laptops (C → L)
This conclusion tries to connect 'Copies' and 'Laptops'. The statements linking them are "Some copies are pillows" and "Some pillows are laptops". The middle term is 'Pillows'. We have C → P and P → L. Based on the rules of syllogism involving 'Some' statements, a 'Some' relationship between A and B, and a 'Some' relationship between B and C does not necessarily guarantee any relationship between A and C. There might be a connection, but it is not a logical necessity. Therefore, Conclusion I does not logically follow.
Evaluating Conclusion II: Some pillows are pens (P → S)
This conclusion tries to connect 'Pillows' and 'Pens'. The statements linking them are "Some pillows are laptops" and "Some laptops are pens". The middle term is 'Laptops'. We have P → L and L → S. Similar to Conclusion I, two 'Some' statements (P → L and L → S) do not guarantee a 'Some' relationship between the end terms (P and S). Therefore, Conclusion II does not logically follow.
Evaluating Conclusion III: Some pens are laptops (S → L)
This conclusion tries to connect 'Pens' and 'Laptops'. Let's look at Statement 3: "Some laptops are pens" (L → S). The conclusion is "Some pens are laptops" (S → L). In syllogism, an 'I' proposition (Some A are B) can be validly converted to an 'I' proposition with the terms swapped (Some B are A). If "Some laptops are pens" is true, then it logically follows that "Some pens are laptops" must also be true. Therefore, Conclusion III logically follows from Statement 3.
Evaluating Conclusion IV: Some pens are pillows (S → P)
This conclusion tries to connect 'Pens' and 'Pillows'. The statements linking them are "Some laptops are pens" and "Some pillows are laptops". We have L → S and P → L. Rearranging the order of statements doesn't change the logic. The statements are P → L and L → S. This is the same structure as evaluating Conclusion II (connecting P and S). As explained before, two 'Some' statements (P → L and L → S) do not guarantee a 'Some' relationship between the end terms (P and S). Therefore, Conclusion IV does not logically follow.
Summary of Conclusions
| Conclusion | Logical Follows? | Reasoning |
|---|---|---|
| I. Some copies are laptops. | No | C → P, P → L does not guarantee C → L. |
| II. Some pillows are pens. | No | P → L, L → S does not guarantee P → S. |
| III. Some pens are laptops. | Yes | Logically converts from "Some laptops are pens" (Statement 3). |
| IV. Some pens are pillows. | No | P → L, L → S does not guarantee S → P. |
Based on the analysis, only Conclusion III logically follows from the given statements.
Revision Table: Syllogism Rules for 'Some' Statements
| Statement 1 | Statement 2 | Valid Conclusion? | Notes |
|---|---|---|---|
| Some A are B | Some B are C | None necessarily follows between A and C. | Two 'Some' premises yield no valid conclusion between the extremes. |
| All A are B | Some B are C | None necessarily follows between A and C. | Illicit Minor/Major or undistributed middle term issues can arise. |
| Some A are B | All B are C | Some A are C | This combination can yield a 'Some' conclusion. |
| No A are B | Some B are C | Some C are not A | This combination can yield a 'Some...not' conclusion. |
| Some A are B (I) | - | Some B are A (I) | Valid simple conversion of an 'I' proposition. |
Note: The statements in this problem are all of the "Some A are B" type. The first row of the table shows that two such statements connecting terms (A-B, B-C) do not logically force a connection between the outer terms (A and C).
Additional Information on Syllogism and Logical Reasoning
Syllogism is a type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are assumed to be true. These problems test your ability to follow logical structure, not your knowledge of common facts.
- Categorical Propositions: Syllogism uses categorical propositions like All A are B, No A are B, Some A are B, Some A are not B.
- Terms: Each syllogism has a major term, a minor term, and a middle term. The middle term connects the other two in the premises but doesn't appear in the conclusion.
- Validity vs. Truth: A syllogism is valid if its conclusion logically follows from its premises, regardless of whether the premises or conclusion are factually true. In these questions, you assume the statements are true and check for logical validity of the conclusions.
- Common Fallacies: Errors in syllogism often involve an undistributed middle term or drawing a universal conclusion from particular premises.
Solving syllogism problems correctly requires careful analysis of the structure and adherence to the rules of deduction, ignoring external knowledge.
Similar Questions
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 teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
Two 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 follow(s) from the statements.
Statements:
All keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
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 switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
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 follow(s) from the statements.
Statements:
All H are G.
All V are H.
Some V are I.
Conclusions:
I. At least some G are I.
II. All I being H is a possibility.
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 beds are chairs.
Some chairs are tables.
All tables are cupboards.
Conclusions :
I. Some tables are beds.
II. Some cupboards are chairs.
III. Some cupboards are beds.
Read the given statement(s) 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 statement(s).
Statements :
Some ceilings are beds.
No bed is an apple.
All dogs are beds.
Conclusions :
I. Some ceilings being dogs is a possibility.
II. No dog is an apple.
III. All beds are dogs.
IV. No ceiling is an apple.
Two 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 follow(s) from the statements.
Statements:
All keys are locks.
All locks are handles.
Conclusions:
I. All locks are keys.
II. All handles are keys.
Two 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 follow(s) from the statements.
Statements:
Some windows are doors.
No window is a cupboard.
Conclusions:
I. No cupboard is a door.
II. Some doors are definitely not cupboard.
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) Some trousers are pants.
2) All pants are jeans.
3) All jeans are coats.
Conclusions:
I. All pants are coats.
II. At least some trousers are jeans
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 follow(s) from the statements.
Statements :
No crow is a monkey.
All monkeys are turtles.
No turtle is a snail.
Conclusions :
I. Some snails being crows is a possibility.
II. No turtle is a crow.
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
In the question two statements are given, followed by three conclusions, I, II and III. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : Some cars are scooters.
Statement 2 : All scooters are buses.
Conclusion I : Some scooters are cars.
Conclusion II : Some buses are cars.
Conclusion III : All cars are buses.
Read the given statements and conclusions carefully. Assuming that the information in the statement is true even if they appear to be at variance with commonly known facts, choose the conclusion that logically follows from the statement beyond reasonable doubt.
Statement:-
1. Some dogs are cats.
2. All cats are birds.
Conclusion:-
1. Some dogs are birds.
2. No cat is dog.
