In this question, 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 follows/follow from the statements. Statements: Some roses are yellow. Some yellow are buses. All buses are green. Conclusions: I. All yellow are roses. II. Some buses are yellow. III. All yellow are green.
Only conclusion II follows.
Understanding Syllogism Statements and Conclusions
This question asks us to analyze three statements and determine which of the given conclusions logically follows from them, assuming the statements are true.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: Some roses are yellow.
- Statement 2: Some yellow are buses.
- Statement 3: All buses are green.
These are statements expressing relationships between different categories (roses, yellow things, buses, green things).
Evaluating the Conclusions
Now, let's examine each conclusion based on the statements:
Conclusion I: All yellow are roses.
Statement 1 tells us "Some roses are yellow". This means there is at least one rose that is yellow, or at least one yellow thing that is a rose. However, this does not give us any information about *all* yellow things. It is possible that many yellow things are not roses. For example, yellow could include bananas, lemons, etc. Therefore, we cannot conclude that all yellow things are roses based only on "Some roses are yellow".
This conclusion does not follow.
Conclusion II: Some buses are yellow.
Statement 2 says "Some yellow are buses". In logic, a statement of the form "Some A are B" is equivalent to "Some B are A". If some yellow things are buses, it logically follows that some buses must be yellow. The existence of even one thing that is both yellow and a bus makes both statements true.
Let's illustrate with a simple example:
- If the group 'Yellow' contains {Car, Bus, Shirt} and the group 'Buses' contains {Bus, Van}, then 'Some yellow are buses' is true because 'Bus' is in both groups.
- Conversely, 'Some buses are yellow' is also true because 'Bus' is in both groups.
This conclusion logically follows from Statement 2.
Conclusion III: All yellow are green.
We have Statement 2: "Some yellow are buses", and Statement 3: "All buses are green".
From Statement 2, we know there's an overlap between 'yellow' and 'buses'. From Statement 3, we know everything that is a 'bus' is also 'green'.
Combining these:
- There is a part of 'yellow' that is also 'bus'.
- That part of 'yellow' (which is 'bus') must also be 'green' because all buses are green.
This leads to the conclusion that "Some yellow are green". However, the conclusion presented is "All yellow are green". Just because some yellow things are green does not mean all yellow things are green. For example, a yellow banana is yellow, but it is not a bus and therefore not guaranteed to be green (in the context of buses being green).
This conclusion does not follow.
Summary of Conclusions
Based on our analysis:
- Conclusion I (All yellow are roses) - Does not follow.
- Conclusion II (Some buses are yellow) - Follows.
- Conclusion III (All yellow are green) - Does not follow.
Therefore, only conclusion II logically follows from the given statements.
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| I. All yellow are roses. | No | Statements only say "Some roses are yellow", not vice versa for "All yellow". |
| II. Some buses are yellow. | Yes | This is the converse of "Some yellow are buses" (Statement 2), which is logically equivalent. |
| III. All yellow are green. | No | Statements imply "Some yellow are green", not "All yellow are green". |
Revision Table: Syllogism Basics
| Statement Type | Form | Conversion (Simple) |
|---|---|---|
| Universal Affirmative (A) | All S are P | Cannot convert simply (Some P are S) |
| Universal Negative (E) | No S are P | No P are S |
| Particular Affirmative (I) | Some S are P | Some P are S |
| Particular Negative (O) | Some S are not P | Cannot convert simply |
In this problem, Conclusion II is the simple conversion of Statement 2 ("Some yellow are buses" <=> "Some buses are yellow").
Additional Information: Venn Diagrams in Logic
Venn diagrams are useful tools for visualizing the relationships described in syllogism statements. Each category is represented by a circle, and the overlap between circles represents the elements that belong to both categories.
- "All S are P": The circle for S is completely inside the circle for P.
- "No S are P": The circles for S and P do not overlap.
- "Some S are P": The circles for S and P overlap, and there is at least one element in the overlapping region (often marked with an 'x').
- "Some S are not P": The circle for S has an area outside the overlap with P, and there is at least one element in that area (marked with an 'x').
By drawing diagrams for the statements, you can visually check if the conclusions hold true in all possible valid diagrams.
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 follow(s) from the statements.
Statements:
1. All rugs are blankets.
2. All blankets are pillows.
3. Some blankets are frames.
Conclusions:
I. All pillows are rugs.
II. Some pillows are rugs.
III. All rugs are frames
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. All T are G.
II. All G are H.
Conclusions:
I. All T are H.
II. No G is T.
III. All H are G.
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 reds are pinks.
All whites are pinks.
All pinks are oranges.
Conclusions:
I. All whites are oranges.
II. All oranges are reds.
III. Some oranges are whites.
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. All R are M.
II. All L are M.
Conclusions:
I. Some M are not R.
II. Some L are R.
III. Some M are L.
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. All M are A.
II. No A is R.
Conclusion:
I. No M is R.
II. Some A are M.
III. Some R are A.
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 c are f.
No f is t.
All p are c.
Conclusions:
I. Some t are c.
II. No p is t.
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 bottles are towels.
No towel is a pillow.
All bottles are coats.
Conclusions:
I. Some coats are towels.
II. No coat is a towel.
III. Some bottles are pillows.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 Tim are Jack.
No Jack is Ben.
Some Ben is Ruth.
Conclusions:
I. No Ruth is Jack.
II. Some Ben are Jack.
III. No Ben is Tim.
- Sunita travels 6 Km towards north east. Then travels 9 Km towards west. From there, she goes 6 Km south-west and finally goes 3 Km towards east. How far is she from her initial position?
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 laptops are phones.
Some phones are capsules.
Some capsules are pens.
Conclusions:
I. Some laptops are capsules.
II. Some phones are pens.
III. Some pens are capsules.
IV. Some pens are phones.
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.
In the question below are given three statements followed by two conclusions. You have to take each of the given statements to be true. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
Some schools are colleges.
No college is university.
All universities are hospitals.
Conclusions:
I. Some schools are universities.
II. At least some hospitals are colleges.
