Statement:
All oranges are fruits. No fruit is a vegetable. All vegetables are green.
Conclusions:
I. No orange is green.
II. No orange is a vegetable.
Logical Reasoning Solution
This problem requires analyzing a set of statements and determining which conclusions logically follow using principles of syllogism.
Statement Analysis
- Statement 1: All oranges are fruits. (Symbolically: $\forall x (\text{Orange}(x) \implies \text{Fruit}(x))$)
- Statement 2: No fruit is a vegetable. (Symbolically: $\forall x (\text{Fruit}(x) \implies \neg \text{Vegetable}(x))$ or $\text{Fruit} \cap \text{Vegetable} = \emptyset$)
- Statement 3: All vegetables are green. (Symbolically: $\forall x (\text{Vegetable}(x) \implies \text{Green}(x))$ or $\text{Vegetable} \subseteq \text{Green}$)
Conclusion Analysis
Conclusion I: No orange is green.
We need to determine if ($\forall x (\text{Orange}(x) \implies \neg \text{Green}(x))$) follows.
- From Statements 1 and 2, we deduce that no orange is a vegetable ($\forall x (\text{Orange}(x) \implies \neg \text{Vegetable}(x))$).
- Statement 3 implies that the set of vegetables is a subset of the set of green things ($\text{Vegetable} \subseteq \text{Green}$).
- This relationship does not exclude the possibility that non-vegetables (like oranges, which are fruits) could also be green. The set 'Green' might contain items that are not vegetables.
- Therefore, Conclusion I does not necessarily follow from the given statements.
Conclusion II: No orange is a vegetable.
We need to determine if ($\forall x (\text{Orange}(x) \implies \neg \text{Vegetable}(x))$) follows.
- Statement 1: Oranges $\subseteq$ Fruits.
- Statement 2: Fruits $\cap$ Vegetables = $\emptyset$.
- Since the set of oranges is entirely contained within the set of fruits, and the set of fruits has no overlap with the set of vegetables, it must be true that the set of oranges has no overlap with the set of vegetables.
- Therefore, Conclusion II directly follows from Statements 1 and 2.
Final Result
Only Conclusion II logically follows from the given statements.
Similar Questions
- Read the following statement carefully and identify the conclusion that follows.
Statement:
All poets are writers. Some writers are critics. No critic is a fool.
Conclusions:
I. Some poets are critics.
II. Some writers are not fools. - Statements: All dancers are artists. No artist is lazy.
Conclusions: I. No dancer is lazy. II. Some lazy are dancers. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All kids are students. Some students are athletes. No athlete is a scholar.
Conclusions:
I. Some kids may be athletes.
II. No kid is a scholar. - Statements: Some keys are locks. Some locks are doors.
Conclusions: I. Some keys are doors. II. All locks being keys is a possibility. - Read the following statement carefully and identify the conclusion that follows.
Statement:
All musicians are artists. Some artists are dancers. No dancer is blind.
Conclusions:
I. Some artists are not blind.
II. All blind are not dancers. Statements: Some pens are papers. All papers are books. Conclusions: I. Some pens are books. II. All books are pens.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All birds are animals. Some animals are tigers. No tiger is a bird.
Conclusions:
I. Some tigers are birds.
II. Some animals are not birds.
- Statements: All dogs are cats. Some cats are rats. Conclusions: I. Some rats are dogs. II. All dogs are rats.
Read the following statement carefully and identify the conclusion that follows.
Statement:
All pens are blue things. Some blue things are plastic. No plastic is recyclable.
Conclusions:
I. Some pens are plastic.
II. Some blue things are not recyclable.
Read the following statement carefully and identify the conclusion that follows.
Statement:
No apple is blue. All oranges are apples.
Conclusions:
I. No orange is blue.
II. Some apples are oranges.
Important Questions from Syllogism
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 students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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 actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
