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 apples are bananas. Some mangos are apples. Conclusions : (I) Some mangos are bananas. (II) Some bananas are apples.
Only conclusion II follows
Understanding the Logic Reasoning Problem
This question asks us to analyze two statements and determine which of the given conclusions logically follow from them. We must assume the statements are true, even if they contradict common knowledge. This type of problem is based on syllogism, a form of logical argument where a conclusion is inferred from two or more statements (premises).
Analyzing the Statements and Conclusions
Let's break down the given statements and conclusions:
Statements:
- Some apples are bananas.
- Some mangos are apples.
Conclusions:
- Some mangos are bananas.
- Some bananas are apples.
Analyzing Conclusion I: Some mangos are bananas.
We are told that some apples are bananas and some mangos are apples. Let's think about the relationship between mangos and bananas based on their connection to apples.
- Statement 1 establishes a partial overlap between the set of apples and the set of bananas.
- Statement 2 establishes a partial overlap between the set of mangos and the set of apples.
We can represent these relationships using diagrams (though we won't draw them explicitly here, we can think about them). The 'some' relationship means there is at least one element common to both sets. However, these statements do not give us any direct or indirect necessary connection between mangos and bananas. It is possible that the apples that are mangos are different from the apples that are bananas. Therefore, there is no guarantee that any mango is also a banana.
Conclusion I, "Some mangos are bananas," does not necessarily follow from the given statements. It might be true, but it is not logically compelled by the statements.
Analyzing Conclusion II: Some bananas are apples.
Let's look at the statements again, specifically Statement 1:
- Statement 1: Some apples are bananas.
This statement explicitly tells us that there is an overlap between the set of apples and the set of bananas. If some apples have the property of being bananas, this implies that there are some members of the set of bananas that have the property of being apples. In other words, the relationship "Some A are B" is symmetrical in terms of overlap – it implies "Some B are A".
Conclusion II, "Some bananas are apples," directly follows from Statement 1. If 'Some apples are bananas' is true, then 'Some bananas are apples' must also be true.
Determining Which Conclusions Follow
Based on our analysis:
- Conclusion I (Some mangos are bananas) does not logically follow from the statements.
- Conclusion II (Some bananas are apples) logically follows from Statement 1.
Therefore, only conclusion II follows from the given statements.
Summary of Conclusions
| Conclusion | Logically Follows? | Reasoning |
|---|---|---|
| I) Some mangos are bananas. | No | Statements provide no necessary link between mangos and bananas. |
| II) Some bananas are apples. | Yes | Directly implied by Statement 1 ("Some apples are bananas"). |
Revision Table: Syllogism Rules for "Some"
| Statement Type | Implication / Conversion |
|---|---|
| Some A are B | Implies Some B are A |
| Some A are B | Does not imply All A are B |
| Some A are B and Some B are C | Does not imply Some A are C |
Additional Information: Understanding Syllogisms
Syllogisms are a core part of deductive reasoning. They consist of premises (statements) and a conclusion. In these problems, the truth of the premises is assumed, and the task is to determine if the conclusion is necessarily true based *only* on those premises.
Keywords like "All", "No", and "Some" define the relationship between categories:
- All: Indicates complete inclusion (e.g., All dogs are mammals).
- No: Indicates complete exclusion (e.g., No fish are birds).
- Some: Indicates at least one, but not necessarily all. It signifies partial inclusion or overlap (e.g., Some students are athletes). "Some" is interpreted as "at least one and possibly all".
Understanding how these keywords interact in different statement combinations is key to solving syllogism problems. The statements "Some A are B" and "Some B are A" are equivalent in terms of the existence of an overlap.
Similar Questions
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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 chairs are cupboards.
Some chairs are radios.
No chair is piano.
Conclusions:
I. Some radios are cupboards.
II. Some cupboards are not piano.
III. Some radios are not piano.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is ture, 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 aero-planes are cars.
All helicopters are cars.
All cars are scooters.
Conclusions:
1. All helicopters are scooters.
2. Some aero-planes are helicopters.
3. No aero-plane is helicopter.
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 books are grapes.
Some grapes are fruits.
Conclusions:
I. No grape is a book.
II. Some grapes are books.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 fans are radio.
All fans are light.
Conclusion I: Some radios are light.
Conclusion II: Some lights are radio.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 scissors are spoons.
All spoons are plates.
Conclusions:
1. Some plates are spoons.
2. Some spoons are scissors.
3. Some plates are scissors.
Read the given statements and conclusions carefully. Assuming that the information given in the statement 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:
No boat is ship.
Some ships are rods.
Conclusions:
I. No boat is rod.
II. Some rods are ships.
III. Some rods are not boats.
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 bottles are glasses.
All glasses are jugs.
Conclusions:
I. All bottles are jugs.
II. All jugs are bottles.
III. Some glasses are bottles.
In the following question below are given some statements followed by some conclusions. 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 pen are black.
II. Some pen are blue.
III. No black is red.
Conclusions:
I. No pen is red.
II. Some blue are black.
III. Some black are pens.In the following question below are given some statements followed by some conclusions. 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 cups are plates.
II. All plates are red.
Conclusions:
I. All cups are red.
II. All plates are cups.
III. All red are plates.In the following question below are given some statements followed by some conclusions. 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 sky are blue.
II. Some blue are soft.
Conclusions:
I. Some sky are soft.
II. Some soft are sky.
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.
