Statements:
All bananas are apples.
All apples are grapes.
Some grapes are oranges.
Conclusions:
(I) All grapes are bananas.
(II) All oranges are apples.
Logical Reasoning: Analyzing Statements and Conclusions
Statement Analysis
We are given three statements:
- Statement 1: All bananas are apples. (All B are A)
- Statement 2: All apples are grapes. (All A are G)
- Statement 3: Some grapes are oranges. (Some G are O)
From Statement 1 and Statement 2, using the principle of syllogism (transitivity), we can logically deduce:
- All bananas are grapes (All B are G).
This means the set of 'bananas' is entirely contained within the set of 'apples', which itself is entirely contained within the set of 'grapes'.
Conclusion Analysis
Let's evaluate each conclusion based on the statements:
Conclusion (I): All grapes are bananas
- We derived that All bananas are grapes (All B are G).
- Conclusion (I) states the reverse: All grapes are bananas (All G are B).
- This does not logically follow. Just because all bananas are grapes does not mean every grape must be a banana. There can be grapes that are not bananas.
Conclusion (II): All oranges are apples
- Statement 3 tells us Some grapes are oranges (Some G are O).
- We know All apples are grapes (All A are G). This means the set 'Apples' is a subset of 'Grapes'.
- However, the 'some grapes' that are 'oranges' might be from the part of the 'Grapes' set that does not overlap with the 'Apples' set.
- We cannot conclude that these specific 'orange grapes' must also be 'apples'.
Final Decision
Since neither Conclusion (I) nor Conclusion (II) can be logically derived from the given statements, the correct option is 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
