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.
Similar Questions
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.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. Some Z are X.
II. Some W are Z.
Conclusions:
I. Some X are not W.
II. Some X are not Z.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some mobiles are flat.
All flats are TVs.
Some TVs are plastic.
Conclusions:
I. Some mobiles are TVs.
II. Some flats are plastic.
III. All plastic are TVs.
Three statements are given, followed by three conclusions numbered I, II and III.Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
No cup is a plate.
All cups are utensils.
Some bottles are cups.
Conclusions:
I. Some utensils are not plates.
II. Some bottles are not plates.
III. No bottle is a plate.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements.
Statements:
Some watches are projectors.
All projectors are lamps.
Some heaters are watches.
Conclusions:
(I) Some heaters are projectors.
(II) Some lamps are heaters.
(III) All watches are lamps
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. No A is B.
II. No C is B.
Conclusion:
I. Some C are not A.
II. Some A are B.
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 benches are tables.
Some tables are chairs.
Some chairs are pencils.
Conclusions:
I. Some benches are chairs.
II. Some tables are pencils.
III. Some pencils are chairs.
IV. Some pencils are tables.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
