In the following questions, two statements S1 & S2 are given followed by two conclusions I & II. Taking the two statements S1 and S2 as true, decide which one of the answer (A), (B), (C), (D) logically follows.
Statements : S1 : Renu can understand the problem quickly. S2 : Mathematics students have good reasoning ability. Conclusions : I : Renu has good reasoning ability. II : Renu is a Mathematics student
Neither I nor II follows.
Logical Reasoning Problem Analysis
This question requires us to analyze two given statements, S1 and S2, and then determine which of the two provided conclusions, Conclusion I and Conclusion II, logically follows from these statements. In deductive reasoning, we must only draw conclusions that are strictly and necessarily implied by the given premises, assuming the premises are true.
Statements Breakdown
- Statement S1: "Renu can understand the problem quickly."
- This statement tells us about a specific skill or characteristic of an individual named Renu. It highlights her efficiency in grasping problems.
- Statement S2: "Mathematics students have good reasoning ability."
- This statement describes a general attribute of a particular group: Mathematics students. It establishes a link between being a Mathematics student and possessing good reasoning ability.
Conclusion Evaluation
Evaluating Conclusion I: "Renu has good reasoning ability."
Let's carefully examine if this conclusion can be derived from the given statements:
- S1 tells us that Renu understands problems quickly. However, understanding problems quickly does not automatically or necessarily imply that one has good reasoning ability. While often correlated, they are not presented as equivalent or directly causative in the statements.
- S2 states that Mathematics students have good reasoning ability. For us to conclude that Renu has good reasoning ability based on S2, we would first need to know if Renu is a Mathematics student. The statements do not provide any information to confirm that Renu is indeed a Mathematics student.
Since there is no direct logical connection established between Renu's quick understanding of problems and her having good reasoning ability, and we cannot confirm she is a Mathematics student, Conclusion I does not logically follow.
Evaluating Conclusion II: "Renu is a Mathematics student."
Now, let's assess if this conclusion is supported by the statements:
- S1 informs us about Renu's ability to understand problems quickly. This skill is not unique to Mathematics students; many people from various fields can understand problems quickly. This statement does not provide any basis to classify her as a Mathematics student.
- S2 describes a characteristic of Mathematics students (having good reasoning ability). However, this statement defines a trait of Mathematics students; it does not say that anyone who understands problems quickly or has good reasoning ability *must* be a Mathematics student. The statements do not provide any evidence or information that directly identifies Renu as belonging to the group of Mathematics students.
Therefore, based solely on the given statements, we cannot conclude that Renu is a Mathematics student. This conclusion does not logically follow.
Logical Deduction Summary
In logical reasoning, conclusions must be an undeniable consequence of the premises. We cannot make assumptions or introduce outside information.
- The ability to understand a problem quickly (S1) does not guarantee good reasoning ability for everyone, nor does it make someone a Mathematics student.
- While Mathematics students have good reasoning ability (S2), this does not mean everyone with good reasoning ability, or everyone who understands problems quickly, is a Mathematics student.
Since neither Conclusion I nor Conclusion II can be definitively and directly inferred from the provided statements, neither conclusion logically follows.
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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
