Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some cars are bikes.
All bikes are trucks.
Conclusions:
(I) Some trucks are cars.
(II) All trucks are cars.
Only conclusion (I) follows
Analyzing Statements and Conclusions about Cars, Bikes, and Trucks
This problem requires us to analyze two given statements and determine which of the provided conclusions logically follow from them. We must assume the statements are true, even if they seem unusual.
Analyzing Statement 1: Some cars are bikes
This statement tells us that there is at least one car that is also a bike. The set of 'cars' and the set of 'bikes' have a non-empty intersection. In logical terms, we can represent this as:
\( \text{Cars} \cap \text{Bikes} \neq \emptyset \)
This means there's an overlap between these two categories.
Analyzing Statement 2: All bikes are trucks
This statement indicates that every single bike is also a truck. The entire set of 'bikes' is contained within the set of 'trucks'. We can represent this as:
\( \text{Bikes} \subseteq \text{Trucks} \)
This means the 'Bikes' category is a subset of the 'Trucks' category.
Evaluating Conclusion (I): Some trucks are cars
Let's see if this conclusion follows. We know from Statement 1 that some cars are bikes (\( \text{Cars} \cap \text{Bikes} \neq \emptyset \)). We also know from Statement 2 that all these bikes are trucks (\( \text{Bikes} \subseteq \text{Trucks} \)).
Since the cars that are bikes are definitely trucks (because all bikes are trucks), it logically follows that those specific vehicles are both trucks *and* cars. Therefore, there must be some trucks that are also cars.
Using set notation, if \( \text{Cars} \cap \text{Bikes} \neq \emptyset \) and \( \text{Bikes} \subseteq \text{Trucks} \), then the elements in \( \text{Cars} \cap \text{Bikes} \) must also be in \( \text{Trucks} \). This implies that \( \text{Cars} \cap \text{Trucks} \neq \emptyset \).
Thus, Conclusion (I) logically follows from the statements.
Evaluating Conclusion (II): All trucks are cars
Now let's consider if all trucks are necessarily cars. We know that the set of bikes is within the set of trucks (\( \text{Bikes} \subseteq \text{Trucks} \)), and that some cars overlap with bikes (\( \text{Cars} \cap \text{Bikes} \neq \emptyset \)).
However, the set of trucks (\( \text{Trucks} \)) could potentially be much larger than the set of bikes (\( \text{Bikes} \)). There might be many trucks that are not bikes. Statement 1 only establishes a connection between *some* cars and bikes, not all cars or all trucks. We cannot conclude that the entire set of trucks is contained within the set of cars. For example, there could be trucks that are not bikes and also not cars.
Therefore, Conclusion (II) does not logically follow from the given statements.
Final Deduction
Based on the analysis:
- Conclusion (I) logically follows.
- Conclusion (II) does not logically follow.
Therefore, only conclusion (I) is valid.
Similar Questions
Consider the given statements true and decide which of the given conclusion(s) logically follow(s) from the statements.
Statements:
1. All reds are yellows.
2. Some yellow are not greens.
Conclusions:
1. Some yellow are reds
2. All yellow are greens
Consider the given statements to be true and decide which of the conclusions logically follow(s) from the given statements.
Statement:
All fruits are trees. Some trees are birds.
Conclusions:
1. Some birds are trees.
2. Some trees are fruits.
Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some gold are silver.
Some silver are diamonds.
Conclusions:
(I) Some diamonds are gold.
(II) Some silver are gold.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
No dogs are pigs.
All pigs are stones.Conclusions:
(I) Some stones are pigs.
(II) No stones are dogs.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
All chairs are tables.
No table is a bed.Conclusions:
(I) Some beds are chairs.
(II) No bed is a table.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some keys are pens.
All pens are watches.
Conclusions:
(i) Some watches are keys.
(II) All watches are pens.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
All flowers are diamonds.
Some clips are flowers.
Conchisions:
(I) Alll diamonds are clips.
(II) Some diamonds are flowers.Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some bulbs are sands.
All bulbs are candles.
Conclusion:
(I) Some candles are bulbs.
(II) No candle is a sand.
- 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 conclusion(s) logically follow(s) from the statements. Statements: Some cats are rats. All bats are tables. All rats are bats. Conclusions: (I): Some cats are bats. (II): All bats are rats.
Consider the given statement to be true and decide which of the conclusions logically follows (s) from the statements.
Statements:
Some angels are gods.
All living being are gods.
Conclusions:
1. Some gods are angels.
2. Some living beings are gods.
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.
