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)
- 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. - 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:
Some canals are rivers.
Some rivers are oceans.
Some oceans are ponds.
Conclusions:
(I) All ponds are rivers.
(II) All oceans are canals. Take the given statements to be true even if they seem to be at variance with commonly known facts. Then decide which of the given conclusions logically follow the given statements.
Statements :
0% chairs are tables.
All computers are chairs.
Some books are tables.
Conclusions :
I. Not a single table is a computer.
II. Some books are not chairs.
Directions: Study the following Bar-chart and the data provided to answer the questions that follow: Sales of 3-different companies selling T-Shirts for the years from 2006 to 2009 are given. How much percentage of sales decreased for Brand X T-shirt in 2009 compared with 2007?
Statements:
All herbivores are carnivores.
Some carnivores are omnivores.
Conclusions:
i) Some herbivores are omnivores.
ii) Some carnivores are herbivores.
