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.
Logic Analysis of Given Statements
We are given three statements and two conclusions. We need to determine which conclusion logically follows from the statements.
Statements Analysis
- Statement 1: Some Apples are Banana.
- This means there is an overlap between the set of Apples and the set of Bananas. At least one Apple is a Banana.
- Statement 2: Some bananas are Grapes.
- This means there is an overlap between the set of Bananas and the set of Grapes. At least one Banana is a Grape.
- Statement 3: No Grape is Book.
- This means the set of Grapes and the set of Books are completely separate (disjoint). If something is a Grape, it cannot be a Book.
Conclusion I Analysis: Some Apples are Book is a possibility.
Let's analyze if it's possible for some Apples to be Books without contradicting the given statements.
- From Statement 1, we know some items belong to both 'Apples' and 'Bananas'. Let's call this overlapping group AB.
- From Statement 2, we know some items belong to both 'Bananas' and 'Grapes'. Let's call this overlapping group BG.
- From Statement 3, we know that anything in the 'Grapes' set cannot be in the 'Books' set. Since the items in BG are Grapes, they cannot be Books.
- However, the premises do not establish any direct relationship between 'Apples' and 'Books'. The overlap AB (Apples that are Bananas) might be entirely different from the overlap BG (Bananas that are Grapes).
- It is possible that the items in the AB group (which are Apples and Bananas) are not Grapes. If an item is an Apple and a Banana, but not a Grape, then Statement 3 (No Grape is Book) does not prevent it from being a Book.
- Therefore, we can imagine a scenario where an item is an Apple, a Banana, and also a Book, without violating any of the given statements. This makes Conclusion I a possibility.
Conclusion II Analysis: All Bananas are Book.
Let's analyze if this conclusion must be true.
- From Statement 2, we know that "Some bananas are Grapes".
- From Statement 3, we know that "No Grape is Book".
- Combining these, we can deduce that the specific bananas which are also Grapes *cannot* be Books.
- This directly implies that "Some Bananas are not Book".
- Therefore, the conclusion "All Bananas are Book" cannot be true, as we have identified at least some bananas that are definitely not books.
Final Conclusion
Based on the analysis:
- Conclusion I ("Some Apples are Book is a possibility") can be true without contradicting the premises.
- Conclusion II ("All Bananas are Book") is false because the premises allow us to prove that some bananas are not books.
Thus, only Conclusion I follows (as a possibility).
Important Questions from Syllogism (Notes)
- 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 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 furs are rabbits.
All furs are plants.
Conclusions:
(I): Some rabbits are plants.
(II): All plants are furs.
