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 girls are engineers. All engineers are soldiers. No doctor is a girl. Conclusions: I. No soldier is a girl. II. No girl is an engineer. III. Some soldiers are engineers.
Only conclusion III follows.
Understanding the Syllogism Statements and Conclusions
This question requires us to analyze logical statements and determine which conclusions logically follow from them, assuming the statements are absolutely true, even if they contradict common knowledge. We will examine each statement and conclusion carefully.
The given statements are:
- Statement 1: Some girls are engineers.
- Statement 2: All engineers are soldiers.
- Statement 3: No doctor is a girl.
The given conclusions are:
- Conclusion I: No soldier is a girl.
- Conclusion II: No girl is an engineer.
- Conclusion III: Some soldiers are engineers.
Analyzing Statement Combinations
We can analyze how the statements relate to each other using logical deduction or conceptualizing with Venn diagrams.
Let's combine Statement 1 and Statement 2:
- Some girls are engineers. (G ∩ E ≠ ∅)
- All engineers are soldiers. (E ⊆ S)
If some girls are engineers, and all engineers are soldiers, then it logically follows that some of those girls who are engineers must also be soldiers. Therefore, "Some girls are soldiers" is a valid deduction from Statements 1 and 2.
From Statement 2 alone ("All engineers are soldiers"), we can deduce its conversion. The conversion of "All E are S" is "Some S are E". This means "Some soldiers are engineers" is a valid deduction directly from Statement 2.
Statement 3 ("No doctor is a girl") introduces a third category (doctors) but doesn't directly connect girls, engineers, or soldiers in a way that helps evaluate Conclusions I, II, or III which only involve girls, engineers, and soldiers.
Evaluating Each Conclusion Based on Statements
Analyzing Conclusion I: No soldier is a girl
Based on our analysis of Statement 1 ("Some girls are engineers") and Statement 2 ("All engineers are soldiers"), we deduced that "Some girls are soldiers". This deduction directly contradicts Conclusion I, which states that "No soldier is a girl" (meaning no girl is a soldier). Therefore, Conclusion I does not logically follow from the given statements.
Analyzing Conclusion II: No girl is an engineer
Let's look at Statement 1: "Some girls are engineers". This statement explicitly affirms that there is an intersection between the categories of girls and engineers. Conclusion II, however, states that "No girl is an engineer", which means there is no intersection between girls and engineers. Since Statement 1 directly contradicts Conclusion II, Conclusion II does not logically follow from the given statements.
Analyzing Conclusion III: Some soldiers are engineers
Consider Statement 2: "All engineers are soldiers". This means that every single individual who is an engineer is also a soldier. If this is true, then there must be at least one engineer (implied by "Some girls are engineers" having an existing subject), and that engineer is a soldier. Therefore, it must be true that "Some soldiers are engineers". This is a direct logical inference (conversion) from a Universal Affirmative statement.
Summary of Conclusion Evaluation
Let's summarize our findings for each conclusion:
| Conclusion | Stated | Logical Follows? | Reasoning |
|---|---|---|---|
| I | No soldier is a girl. | No | Statements 1 & 2 imply "Some girls are soldiers", which contradicts Conclusion I. |
| II | No girl is an engineer. | No | Statement 1 says "Some girls are engineers", which contradicts Conclusion II. |
| III | Some soldiers are engineers. | Yes | Statement 2 says "All engineers are soldiers". The conversion of "All E are S" is "Some S are E". |
Based on this analysis, only Conclusion III logically follows from the given statements.
Revision Table for Syllogism Rules
| Statement Type | Format | Conversion |
|---|---|---|
| Universal Affirmative (A) | All P are Q | Some Q are P (Simple Conversion is not always valid, Conversion per Accidens is valid if P exists) |
| Universal Negative (E) | No P is Q | No Q is P (Simple Conversion is valid) |
| Particular Affirmative (I) | Some P are Q | Some Q are P (Simple Conversion is valid) |
| Particular Negative (O) | Some P are not Q | Conversion is generally not valid |
In this problem, Statement 2 is "All engineers are soldiers" (All E are S). Its conversion per accidens is "Some soldiers are engineers" (Some S are E), which is exactly Conclusion III. Statement 1 is "Some girls are engineers" (Some G are E). Its conversion is "Some engineers are girls" (Some E are G).
Additional Information on Logical Reasoning
Logical reasoning questions, particularly syllogisms, test your ability to follow strict rules of inference. It is crucial to:
- Accept the statements as absolutely true, disregarding real-world facts.
- Analyze the structure of the statements (Universal Affirmative, Universal Negative, Particular Affirmative, Particular Negative).
- Understand valid logical operations like conversion, obversion, and contraposition, although conversion is most relevant here.
- Combine statements step-by-step if necessary, identifying the middle term (the term common to two statements that links them, e.g., 'engineers' links Statement 1 and 2).
- Evaluate each conclusion solely based on whether it must be true if the statements are true.
Practicing with Venn diagrams can often help visualize the relationships described in the statements and check the validity of conclusions, especially for those new to formal logic.
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.
