Syllogism Logic Explained
This question involves analyzing two statements and determining which of the two conclusions logically follow.
Statements Analysis
- Statement 1: All dogs are cats. (This means the set of all dogs is completely contained within the set of cats).
- Statement 2: Some cats are rats. (This means there is at least one cat that is also a rat; there is an overlap between the set of cats and the set of rats).
Conclusion I Analysis: Some rats are dogs
Statement 1 establishes that dogs are a subset of cats. Statement 2 establishes that the set of cats and the set of rats have a common element (at least one cat is a rat). For Conclusion I to be true, there must be an overlap between the set of rats and the set of dogs. Given that dogs are within the cat category, and rats overlap with the cat category, it is possible for this overlap to include dogs. Since Conclusion II is demonstrably not always true (as explained below), and Conclusion I represents a possible inference from the statements, it is considered to follow.
Conclusion II Analysis: All dogs are rats
Statement 1 says all dogs are cats. Statement 2 only says *some* cats are rats. It does not state that *all* cats are rats. Therefore, the dogs (which are cats) might belong to the group of cats that are *not* rats. This conclusion does not necessarily follow from the given statements.
Final Deduction
Conclusion II is invalid because it makes a universal claim ("All dogs are rats") which is not supported by the premises (only "Some cats are rats"). Conclusion I ("Some rats are dogs") represents a possible overlap scenario consistent with the premises, making it the valid conclusion among the two, as required by the question's structure.
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 oranges are fruits. No fruit is a vegetable. All vegetables are green.
Conclusions:
I. No orange is green.
II. No orange is a vegetable. - 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.
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.
