Directions: In the following questions, few statements are given and these statements are followed by two conclusions numbered i and ii. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Choose, (A) Only (i) conclusion follows (B) Only (ii) conclusion follows (C) Neither (i) nor (ii) follows (D) Both (i) and (ii) follow (E) Either (i) or (ii) follows
Statements: All herbivores are carnivores. Some carnivores are omnivores. Conclusions: i) Some herbivores are omnivores. ii) Some carnivores are herbivores.
Analyzing the Statements
We are given two statements and need to determine which conclusions logically follow. Let H represent Herbivores, C represent Carnivores, and O represent Omnivores.
- Statement 1: All herbivores are carnivores. This can be written as $H \subseteq C$.
- Statement 2: Some carnivores are omnivores. This means there is at least one carnivore that is also an omnivore, or $C \cap O \neq \emptyset$.
Evaluating Conclusion (i)
Conclusion i: Some herbivores are omnivores ($H \cap O \neq \emptyset$?).
From Statement 1 ($H \subseteq C$) and Statement 2 ($C \cap O \neq \emptyset$), we cannot be certain that the carnivores which are omnivores are also herbivores. The overlap between Carnivores and Omnivores might exist entirely outside the set of Herbivores.
Therefore, Conclusion (i) does not necessarily follow.
Evaluating Conclusion (ii)
Conclusion ii: Some carnivores are herbivores ($C \cap H \neq \emptyset$?).
Statement 1 clearly states "All herbivores are carnivores" ($H \subseteq C$). If every herbivore is a carnivore, then the set of carnivores must include all herbivores. This directly implies that some carnivores are indeed herbivores.
Therefore, Conclusion (ii) logically follows.
Determining the Correct Option
Since only Conclusion (ii) logically follows from the given statements, the correct option is the one that states only (ii) follows.
This corresponds to Option B.
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. 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 sweets are snacks.
All snacks are crisps.
All crisps are tasty.
Conclusions:
i) All sweets are crisps.
ii) All snacks are tasty.
- In a community, some artists are teachers, no teacher is a painter, all painters are artists, and all teachers are professionals. Then it can be definitely asserted that
