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.
Only conclusion (I) follows.
Analyzing Logical Statements: Keys, Pens, and Watches
This problem requires us to evaluate logical conclusions based on two given statements. We need to determine which conclusions necessarily follow from the statements, treating the statements as true.
Statement Analysis
We are given the following statements:
- Statement 1: Some keys are pens.
- Statement 2: All pens are watches.
Let's break down what these statements mean:
- Statement 1 implies that there is at least one key that is also a pen. The sets of 'keys' and 'pens' overlap.
- Statement 2 implies that every single pen is also a watch. The set of 'pens' is entirely contained within the set of 'watches'.
Conclusion Evaluation
Now, let's evaluate each conclusion based on the statements:
Conclusion (i): Some watches are keys.
Explanation:
- From Statement 1, we know there's an overlap between 'keys' and 'pens'. Let's call the items in this overlap 'key-pens'.
- From Statement 2, we know that all 'pens' (including the 'key-pens') are also 'watches'.
- Therefore, these 'key-pens' are both 'keys' and 'watches'.
- This directly means that there must be some items that are both 'watches' and 'keys'.
- Thus, the conclusion "Some watches are keys" logically follows from the statements.
Conclusion (II): All watches are pens.
Explanation:
- Statement 2 tells us that all pens are watches (Pens ⊆ Watches).
- This does *not* mean the reverse is true. It doesn't state that all watches must be pens.
- It's possible for there to be watches that are not pens, and this wouldn't contradict Statement 2. For example, imagine a set of watches where some are pens, but others are something else entirely (like bracelets). This scenario is consistent with "All pens are watches".
- Since we can imagine scenarios where this conclusion is false while the original statements are true, the conclusion does not logically follow.
Final Deduction
Based on the step-by-step analysis:
- Conclusion (i) logically follows from the given statements.
- Conclusion (II) does not logically follow from the given statements.
Therefore, only conclusion (I) follows.
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 cars are bikes.
All bikes are trucks.
Conclusions:
(I) Some trucks are cars.
(II) All trucks are cars.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:
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.
