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 strainers are knives.
No knife is a pan.
Conclusions:
I. Some pans are strainers.
II. Some knives are strainers.
III. No strainer is a pan
Understanding the Syllogism: Strainers, Knives, and Pans
This question is about logical reasoning, specifically dealing with syllogisms. We need to analyze the given statements and determine which conclusions can be logically derived from them. We assume the statements are true, even if they seem unusual.
Analyzing the Statements
Let's break down the information provided in the statements:
- Statement 1:
All strainers are knives.- This means the entire group of 'strainers' is included within the group of 'knives'. If something is a strainer, it must also be a knife.
- Statement 2:
No knife is a pan.- This means there is absolutely no overlap between the group of 'knives' and the group of 'pans'. If something is a knife, it cannot be a pan, and vice versa.
We can visualize this using sets or Venn diagrams. Imagine a circle for 'Strainers' completely inside a larger circle for 'Knives'. Then, draw a separate circle for 'Pans' that does not touch or overlap with the 'Knives' circle at all.
Evaluating the Conclusions
Now, let's check each conclusion based on our understanding of the statements:
-
Conclusion I:
Some pans are strainers.- From Statement 2, we know that no knife is a pan.
- From Statement 1, we know that all strainers are knives.
- Since all strainers belong to the 'knives' group, and no item in the 'knives' group can be a 'pan', it logically follows that no strainer can be a pan.
- Therefore, the conclusion that 'Some pans are strainers' is false. There is no overlap between pans and strainers.
-
Conclusion II:
Some knives are strainers.- Statement 1 explicitly states:
All strainers are knives. - If every single strainer is also a knife, then it must be true that at least some knives are strainers (specifically, all the ones that happen to be strainers).
- Therefore, this conclusion logically follows from Statement 1.
- Statement 1 explicitly states:
-
Conclusion III:
No strainer is a pan.- As established in the analysis of Conclusion I:
- Statement 1: All Strainers are Knives (S ⊆ K)
- Statement 2: No Knife is a Pan (K ∩ P = ∅)
- If the set of Strainers is entirely within the set of Knives, and the set of Knives has no intersection with the set of Pans, then the set of Strainers cannot have any intersection with the set of Pans.
- Therefore, 'No strainer is a pan' is a valid deduction and logically follows from the statements.
Determining the Correct Option
Based on our analysis:
- Conclusion I does NOT follow.
- Conclusion II DOES follow.
- Conclusion III DOES follow.
Therefore, the only option where both conclusions II and III are stated as following is the correct one.
Comparing this with the given options, Option 1 correctly states that 'Only conclusions II and III follow'.
Similar Questions
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:
No book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
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 rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
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 C are P.
No C is a T.
All P are S.
Conclusions :
I. All S being C is a possibility.
II. At least some T are not C.
III. Some P are not T's.
Three statements are followed by three conclusions numbered I, II, 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 follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
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 tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
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.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
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:
All cups are saucers.
No saucer is a plate.
Conclusions:
I. Some cups are plates.
II. No cup is a plate.
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 cubs are trucks.
All trucks are lanterns.
No lanterns are bricks.
Conclusions:
I. Some cubs are lanterns.
II. Some trucks are not bricks.
III. All cubs are trucks.
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:
No locks are keys.
Some keys are passwords.
Conclusions:
I. Some passwords are locks.
II. All passwords are locks.
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 defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
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.
