In this question, 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 follows/follow from the statements.
Statements:
I. All apples are bees.
II. Some apples are cannons.
III. No cannon is a dear.
Conclusions:
I. Some cannons are bees.
II. No dear is an apple.
Understanding the Syllogism Question
This question tests your ability to analyze logical arguments. You are given three statements and two conclusions. The task is to determine which conclusion(s) logically follow from the statements, assuming the statements are true.
Given Statements and Conclusions
Statements:
- I. All apples are bees.
- II. Some apples are cannons.
- III. No cannon is a dear.
Conclusions:
- I. Some cannons are bees.
- II. No dear is an apple.
Analyzing Statement Relationships
Let's represent the relationships using logical notation:
- Statement I: $\forall x (Apple(x) \implies Bee(x))$ (All apples are bees)
- Statement II: $\exists x (Apple(x) \land Cannon(x))$ (Some apples are cannons)
- Statement III: $\forall x (Cannon(x) \implies \neg Dear(x))$ (No cannon is a dear)
And the conclusions to be evaluated:
- Conclusion I: $\exists x (Cannon(x) \land Bee(x))$ (Some cannons are bees)
- Conclusion II: $\forall x (Dear(x) \implies \neg Apple(x))$ (No dear is an apple)
Step-by-Step Derivation for Conclusion I
We need to check if "Some cannons are bees" logically follows.
- From Statement II, we know that there exists at least one apple that is also a cannon. Let's call this overlapping group 'X'. So, Group X consists of things that are both 'apples' and 'cannons'.
- From Statement I, we know that every single apple is also a bee.
- Since Group X consists of 'apples' (from Statement II), and all 'apples' are 'bees' (Statement I), it logically follows that the things in Group X must also be 'bees'.
- Therefore, Group X represents things that are both 'cannons' (from Statement II) and 'bees' (derived from Statement I & II).
- This directly supports Conclusion I: "Some cannons are bees."
Conclusion I logically follows from Statements I and II.
Step-by-Step Derivation for Conclusion II
We need to check if "No dear is an apple" logically follows.
- Statement III tells us about the relationship between 'cannons' and 'dears' (they are mutually exclusive).
- Statement II connects 'apples' and 'cannons'.
- Combining Statement II and III: We know that the apples which are cannons are definitely not dears. However, Statement II only says *some* apples are cannons. It doesn't provide information about the apples that are *not* cannons.
- There is no information given in the statements that establishes a direct or indirect relationship (like mutual exclusion or inclusion) between the categories 'apples' and 'dears'. We cannot conclude that no dear is an apple based solely on the given statements.
Conclusion II does not logically follow from the given statements.
Final Result
Based on the analysis, only Conclusion I logically follows from the given statements.
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.
