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.
Only conclusion I follows.
Let's analyze the given statements and conclusions using the principles of logical deduction, specifically syllogism. We need to determine which of the conclusions logically follow from the provided statements, assuming the statements are true.
Understanding the Syllogism Statements
We are given three statements:
- Statement 1: Some mobiles are flat. (Relationship between Mobiles and Flat)
- Statement 2: All flats are TVs. (Relationship between Flat and TVs)
- Statement 3: Some TVs are plastic. (Relationship between TVs and Plastic)
These statements establish relationships between different categories: Mobiles, Flat, TVs, and Plastic.
Evaluating Each Conclusion based on Statements
Now, let's examine each conclusion:
Conclusion I: Some mobiles are TVs.
- This conclusion links Mobiles and TVs.
- We look at the statements involving Mobiles and TVs. Statement 1 relates Mobiles and Flat, and Statement 2 relates Flat and TVs.
- Statement 1 says "Some mobiles are flat". This means there is an overlap between the category of Mobiles and the category of Flat. Let's call this overlapping group 'X'. So, these 'X' items are both Mobiles and Flat.
- Statement 2 says "All flats are TVs". This means the entire category of Flat is contained within the category of TVs.
- Since the group 'X' (which is part of Mobiles) is also part of Flat, and all of Flat is part of TVs, it logically follows that the group 'X' must also be part of TVs.
- Therefore, the 'Some mobiles' that are 'flat' must also be 'TVs'.
- So, Conclusion I logically follows from the statements.
Conclusion II: Some flats are plastic.
- This conclusion links Flats and Plastic.
- Statement 2 relates Flat and TVs ("All flats are TVs").
- Statement 3 relates TVs and Plastic ("Some TVs are plastic").
- Statement 2 tells us all Flats are inside the category of TVs.
- Statement 3 tells us there is some overlap between TVs and Plastic.
- However, we don't know if the 'some TVs' that are 'plastic' include any of the TVs that are also 'flats'. It's possible that the overlap between TVs and Plastic happens only in the part of TVs that is *not* Flat.
- Because we cannot definitively conclude from the statements that there is an overlap between Flats and Plastic, Conclusion II does not logically follow.
Conclusion III: All plastic are TVs.
- This conclusion links Plastic and TVs, claiming a universal relationship ("All").
- We look at the statement involving Plastic and TVs: Statement 3 ("Some TVs are plastic").
- Statement 3 only guarantees that there is *at least one* item that is both a TV and plastic (or some overlap exists). It does not provide any information about the entire category of Plastic.
- The statement "Some TVs are plastic" is not the same as "All plastic are TVs". The latter is a converse and is not necessarily true based on the former.
- Therefore, we cannot conclude that Conclusion III logically follows.
Summary of Conclusions
Based on our analysis:
- Conclusion I: Some mobiles are TVs - Follows
- Conclusion II: Some flats are plastic - Does not follow
- Conclusion III: All plastic are TVs - Does not follow
Thus, only Conclusion I logically follows from the given statements.
Revision Table: Syllogism Analysis
| Statements | Conclusions | Follows? | Reasoning |
|---|---|---|---|
| Some A are B | I. Some A are C | Yes | Via Statement 1 & 2: Some A (Mobiles) are B (Flat), and All B (Flat) are C (TVs). The "Some A" that are B must also be C. |
| All B are C | II. Some B are D | No | Via Statement 2 & 3: All B (Flat) are C (TVs), and Some C (TVs) are D (Plastic). The overlap between C and D may or may not include the portion of C that is B. |
| Some C are D | III. All D are C | No | Via Statement 3: Some C (TVs) are D (Plastic). This does not imply that All D (Plastic) are C (TVs). |
Additional Information: Syllogism Rules
Syllogism problems test your ability to deduce conclusions from given statements based on logical rules. Key concepts include:
- Categorical Propositions: Statements like "All A are B," "No A are B," "Some A are B," and "Some A are not B."
- Validity: A syllogism is valid if and only if the conclusion logically follows from the statements, regardless of whether the statements themselves are factually true in the real world.
- Common Pitfalls: Assuming converse statements are true (e.g., concluding "All B are A" from "All A are B"), or assuming relationships exist where none are explicitly stated or necessarily implied (like in Conclusion II).
Practicing with different combinations of statements helps in mastering the logical flow and identifying valid conclusions.
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:
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.
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.
