Statements:
All carrots are beetroots.
No carrot is a ginger.
Conclusions:
(I) Some gingers are beetroots.
(II) All beetroots are gingers.
Statements Analysis
Let's break down the given statements to understand the relationships between the categories: carrots, beetroots, and gingers.
- Statement 1: All carrots are beetroots. This means that the set of all carrots is entirely contained within the set of beetroots. If something is a carrot, it must also be a beetroot. We can represent this as: Carrots $\subseteq$ Beetroots.
- Statement 2: No carrot is a ginger. This means there is absolutely no overlap between the set of carrots and the set of gingers. They are completely separate categories. We can represent this as: Carrots $\cap$ Gingers = $\emptyset$.
Conclusions Evaluation
Now, let's evaluate each conclusion based on the information from the statements.
Conclusion (I): Some gingers are beetroots.
The statements tell us that carrots are a type of beetroot, and carrots are separate from gingers. However, they do not provide any direct information about the relationship between gingers and beetroots as a whole.
- It's possible that the set of gingers and the set of beetroots are completely separate.
- It's also possible that some gingers are beetroots, or even that all gingers are beetroots (as long as those beetroots are not carrots).
- Conversely, it's possible that no gingers are beetroots.
Since we cannot definitively say that there *must* be an overlap between gingers and beetroots based solely on the given statements, Conclusion (I) does not logically follow.
Conclusion (II): All beetroots are gingers.
Let's consider this conclusion. Statement 1 says all carrots are beetroots. Statement 2 says no carrot is a ginger.
If Conclusion (II) were true (all beetroots are gingers), and knowing that all carrots are beetroots (Statement 1), it would logically follow that all carrots must also be gingers. However, Statement 2 explicitly states that "No carrot is a ginger." This creates a direct contradiction.
Therefore, Conclusion (II) cannot possibly be true given the statements.
Final Decision
Based on the analysis:
- Conclusion (I) is not necessarily true.
- Conclusion (II) is demonstrably false given the statements.
Thus, neither conclusion logically follows from the given statements.
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. - 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 bananas are apples.
All apples are grapes.
Some grapes are oranges.
Conclusions:
(I) All grapes are bananas.
(II) All oranges are apples. 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?
