Statements:
All papers are books. All books are erasers. Some erasers are crayons.
Conclusions:
(I) Some papers are crayons.
(II) Some books are crayons.
Analyzing the Syllogism Statements
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:
- All papers are books. (All P are B)
- All books are erasers. (All B are E)
- Some erasers are crayons. (Some E are C)
Derived Relationship:
From statement 1 (All P are B) and statement 2 (All B are E), we can logically deduce that All papers are erasers (All P are E).
Evaluating Conclusion I
Conclusion I: Some papers are crayons. (Some P are C)
We know that all papers are erasers (All P are E) and some erasers are crayons (Some E are C).
This means the set of 'papers' is entirely within the set of 'erasers'. The set of 'erasers' partially overlaps with the set of 'crayons'. However, the 'papers' (which are a subset of 'erasers') might lie in the part of 'erasers' that does *not* overlap with 'crayons'. There is no guarantee of an overlap between 'papers' and 'crayons'.
Therefore, Conclusion I does not necessarily follow.
Evaluating Conclusion II
Conclusion II: Some books are crayons. (Some B are C)
We know that all books are erasers (All B are E) and some erasers are crayons (Some E are C).
Similar to the reasoning for Conclusion I, the set of 'books' is entirely within the set of 'erasers'. The partial overlap between 'erasers' and 'crayons' does not guarantee an overlap between 'books' and 'crayons'. The 'books' could be in the portion of 'erasers' that doesn't include crayons.
Therefore, Conclusion II does not necessarily follow.
Final Determination
Since neither Conclusion I nor Conclusion II logically follows from the given statements, the correct choice is that neither conclusion is valid.
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
