Statements:
All malls are halls. All halls are walls. No mall is a fall.
Conclusions:
(I) No hall is a fall.
(II) No wall is a fall.
Analyzing Statements and Conclusions
We are given three statements and two conclusions. We need to determine if the conclusions logically follow from the statements, assuming the statements are true.
Statements Breakdown
- Statement 1: All malls are halls. (Mall $\subseteq$ Hall)
- Statement 2: All halls are walls. (Hall $\subseteq$ Wall)
- Statement 3: No mall is a fall. (Mall $\cap$ Fall = $\emptyset$)
Deriving Relationships
From Statement 1 and Statement 2, we can logically deduce that all malls are also walls (Mall $\subseteq$ Hall $\subseteq$ Wall).
Evaluating Conclusion I
Conclusion I: No hall is a fall. (Hall $\cap$ Fall = $\emptyset$)
We know that no mall is a fall (Statement 3). However, Statement 1 says all malls are halls. This does not prevent other halls (which are not malls) from potentially being falls. The statements do not provide enough information to conclude that the set of halls and the set of falls are completely separate.
Therefore, Conclusion I does not logically follow.
Evaluating Conclusion II
Conclusion II: No wall is a fall. (Wall $\cap$ Fall = $\emptyset$)
We know that all halls are walls (Statement 2), and thus all malls are walls. We also know no mall is a fall (Statement 3). Similar to Conclusion I, this doesn't exclude the possibility that some walls (which are not halls or malls) could be falls. The statements don't guarantee that the set of walls and the set of falls are disjoint.
Therefore, Conclusion II does not logically follow.
Final Determination
Since neither Conclusion I nor Conclusion II can be definitively proven true based on the given statements, we conclude that neither conclusion follows.
Important Questions from Syllogism (Notes)
Which conclusion would follow the given statements.
Statement:
Some Apples are Banana.
Some bananas are Grapes.
No Grape is Book.
Conclusion:
(I) Some Apples are Book is a possibility.
(II) All Bananas are Book.
In light of the above statements, choose the most appropriate answer from the options given below.- Disregard commonly known facts. Which conclusion would follow on the basis of given statements only.
Statement: Some bottles are car. some cars are cycle.
Conclusion:
(I) Some bottles are cycle is a possibility
(II) All bottles are cycle
In light of the above statements, choose the most appropriate answer from the options given below. - Statements :
All books are cakes.
All cakes are apples.
Conclusions:
I. Some cakes are books
II. No cake is books
III. Some apple are books
IV. All apples are books
Choose the correct option: - All household pets are domestic animals. NO unicorns are domestic animals. Therefore some Unicorns are not household pets. Which type of formal fallacy committed in the above argument ?
- Statements:
Some bags are purses. All purses are containers all containers are suitcases.
Conclusions :
I. Some suitcases are bags
II. All purses are bags
III. All Purses are suitcases
(IV) Some containers are purses
