Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow(s) the given statements. Statements: All eyes are noses. Some noses are lips. Conclusions: I. Some noses are eyes. II. All lips are noses.
Only conclusion I follows
Solving Syllogism Statements and Conclusions
This question asks us to analyze two statements and determine which of the given conclusions logically follow from them, even if the statements contradict known facts. This type of problem falls under deductive reasoning, specifically syllogisms.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: All eyes are noses.
- Statement 2: Some noses are lips.
In terms of categories, we have three classes: Eyes, Noses, and Lips. The statements describe the relationship between these classes.
Evaluating the Conclusions
Now let's look at the conclusions we need to evaluate:
- Conclusion I: Some noses are eyes.
- Conclusion II: All lips are noses.
We need to determine if these conclusions can be derived with certainty from the given statements.
Analyzing Conclusion I: Some noses are eyes
Statement 1 says, "All eyes are noses." This means that the set of 'eyes' is completely contained within the set of 'noses'.
If every single eye is also a nose, then among the group of noses, there must be some noses that are eyes (specifically, all the noses that happen to be eyes). Therefore, the statement "All eyes are noses" directly implies "Some noses are eyes".
Think of it this way: If everyone in Room A is also in Room B, then it must be true that some people in Room B are from Room A. Conclusion I logically follows from Statement 1.
Analyzing Conclusion II: All lips are noses
Statement 2 says, "Some noses are lips." This indicates that there is an overlap between the set of 'noses' and the set of 'lips'. There are some elements that are both noses and lips.
However, Statement 2 does not provide information about all lips. It only tells us about *some* noses being lips, or equivalently, *some* lips being noses (the ones in the overlap). It is possible that the remaining lips are not noses.
For example, if we say "Some students are tall," this doesn't mean that everyone who is tall is a student. Similarly, "Some noses are lips" does not necessarily mean that "All lips are noses". Conclusion II does not logically follow from the statements.
Summary of Analysis
- Conclusion I: Some noses are eyes - This follows from "All eyes are noses".
- Conclusion II: All lips are noses - This does not follow from "Some noses are lips".
Based on this analysis, only Conclusion I is valid.
Determining the Final Answer
Comparing our findings with the options, we see that only Conclusion I follows.
| Statement | Type | Representation (A=Eyes, B=Noses, C=Lips) |
|---|---|---|
| All eyes are noses. | Universal Affirmative (All A are B) | Set A is a subset of Set B. |
| Some noses are lips. | Particular Affirmative (Some B are C) | Sets B and C have at least one element in common. |
| Conclusion | Representation | Follows? | Reason |
|---|---|---|---|
| Some noses are eyes. | Some B are A | Yes | If All A are B, then Some B are A (Immediate inference). |
| All lips are noses. | All C are B | No | 'Some B are C' does not imply 'All C are B'. |
Revision Table: Basic Syllogism Forms and Immediate Inferences
Understanding the immediate inferences from standard categorical propositions is crucial for solving syllogism questions.
| Proposition Type | Form | Example | Immediate Inference (if any) |
|---|---|---|---|
| Universal Affirmative | All S are P | All cats are mammals. | Some P are S (Some mammals are cats). |
| Universal Negative | No S is P | No fish are birds. | No P is S (No birds are fish); All S are not P (All fish are not birds); All P are not S (All birds are not fish). |
| Particular Affirmative | Some S are P | Some students are tall. | Some P are S (Some tall people are students). |
| Particular Negative | Some S are not P | Some animals are not dogs. | No standard immediate inference to swap S and P while retaining form and truth. |
In our problem, "All eyes are noses" is a Universal Affirmative statement. Its immediate inference is "Some noses are eyes", which matches Conclusion I.
"Some noses are lips" is a Particular Affirmative statement. Its immediate inference is "Some lips are noses", which is different from Conclusion II ("All lips are noses").
Additional Information on Syllogism Solving
Syllogism problems involve deductive logic. The conclusions must follow with absolute necessity from the given statements. Here are some key points:
- Truth vs. Validity: We assume the statements are true, regardless of real-world facts. Validity is about whether the conclusion *logically* follows from the statements.
- Venn Diagrams: Drawing Venn diagrams is a popular method. Represent each category with a circle. Shade areas to show "No" relationships and mark areas with an 'X' or shading to show "Some" relationships or "All" relationships (by placing one circle entirely inside another).
- Rules of Syllogism: There are formal rules based on the quantity (All, Some, No) and quality (Affirmative, Negative) of the premises and terms (Subject, Predicate, Middle Term). For example, if both premises are particular ("Some"), no universal conclusion ("All", "No") can follow.
- Middle Term: The term appearing in both statements but not in the conclusion (in this case, 'noses') is the middle term. For a valid conclusion between the other two terms ('eyes' and 'lips'), the middle term must be distributed in at least one premise. 'All A are B' distributes A. 'Some B are C' distributes neither B nor C. 'All A are B' distributes 'eyes'. 'Some B are C' distributes neither 'noses' nor 'lips'. Conclusion I relates 'noses' (B) and 'eyes' (A), terms present in the first statement where 'eyes' is distributed. Conclusion II relates 'lips' (C) and 'noses' (B). Since 'noses' is not distributed in 'Some noses are lips' and 'lips' is not distributed in 'All lips are noses', and 'eyes' is not involved, formal rules confirm Conclusion II is invalid based *only* on the two statements combined regarding 'eyes' and 'lips'. However, as shown, Conclusion I is a direct inference from Statement 1 alone.
Mastering these concepts helps in confidently tackling syllogism questions in various exams.
Similar Questions
Two 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 teachers are engineers.
All clerks are teachers.
Conclusions:
I. Some engineers are clerks.
II. Some teachers are clerks.
III. Some clerks are not engineers.
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 file is a folder.
Some files are PDFs.
All files are Excel sheets.
Conclusions:
I. Some PDFs are folders.
II. Some Excel sheets are folders.
III. Some PDFs are Excel sheets.
In this question three statements are given followed by three conclusions I, II and III. You have to consider the three 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(s) logically follow(s) from the given statements.
Statements:
All photocopiers are computers.
Some computers are laptops.
No laptop is a mobile.
Conclusions:
(I) No computer is a mobile.
(II) Some computers are photocopiers.
(III) All mobiles are photocopiers.
Two Statements are given followed by Two conclusions numbered I and II. 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 paintings are calligraphies.
All sketching are calligraphies .
Conclusions:
I. At least some calligraphies are paintings.
II. No sketching is a painting.
Two statements are given followed by two conclusions numbered I and II. 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 vehicles are helicopters.
All helicopters are cars.
Conclusions:
I. All vehicles are cars.
II. Some vehicles are cars.
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 telescopes are periscopes.
Some telescopes are microscopes.
Some telescopes are kaleidoscopes.
Conclusions:
I. Some kaleidoscopes are telescopes.
II. Some microscopes are kaleidoscopes.
III. Some microscopes are telescopes.
Two statements are given followed by two conclusions numbered I and II. 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 tasks are jobs.
No job is a duty.
Conclusions
I. All tasks can never be duties.
II. Some tasks are duties.
Two statements are given followed by conclusions numbered 1 and 2. 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:
1. Some mammals are animals.
2. All animals are birds.
Conclusions:
1. All birds are animals.
2. Some mammals are birds.
Two statements are given followed by two conclusions numbered I and II. 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 keys are locks.
All locks are handles.
Conclusions:
I. Some locks are keys.
II. Some handles are keys.
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 switches are fans.
No heater is a fan.
Some wires are heaters.
Conclusions:
I. Some wires are fans.
II. No switch is a heater.
III. No wire is a switch.
Important Questions from Conventional Syllogism
In this question, three statements followed by two conclusions numbered I and II have been given. You have to take the given statements to be true even if they seem to be at variance from the commonly facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some flats are apartments.
No apartment is a hall.
Some halls are rooms.
Conclusions: I. At least some rooms are flats.
II. No apartment is a room.
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:
I. Some blue are red.
II. Some green are red.
Conclusions:
I. No blue is green.
II. No red is green.
Given below are two statements, Consider these statements to be true even if they seem factuality absurd, Read the conclusions and then decide which of the given conclusions logically follow(s) from the given statements?
Statements :
1. All vases are flowers.
2. No flowers is a plant.
Conclusions :
1. No vases is a plant.
2. Some plant are vases
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. All A are S.
II. No D is A.
Conclusions:
I. Some S are A.
II. All S are D.
III. No A is D.
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 land are hard.
II. No stone is land.
Conclusions:
I. Some hard are land.
II. Some stone are hard.
