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.
Only conclusions I and III follow
Understanding the Syllogism Problem: Statements and Conclusions
This question is a classic example of a syllogism problem in logical reasoning. We are given three statements and three conclusions. Our task is to determine which of the conclusions logically follow from the given statements, assuming the statements are absolutely true.
The given statements are:
- Some telescopes are periscopes.
- Some telescopes are microscopes.
- Some telescopes are kaleidoscopes.
The given conclusions are:
- Some kaleidoscopes are telescopes.
- Some microscopes are kaleidoscopes.
- Some microscopes are telescopes.
Analyzing the Syllogism Statements
All three statements use the quantifier "Some". A statement like "Some A are B" means there is at least one element that is both A and B. It also implies that the converse statement "Some B are A" is also true. This is a fundamental rule for 'Some' statements in syllogism.
Let's look at the structure of each statement and its implications:
- Statement 1: Some telescopes are periscopes. (Some T are P)
- Statement 2: Some telescopes are microscopes. (Some T are M)
- Statement 3: Some telescopes are kaleidoscopes. (Some T are K)
From these statements, we know there is an overlap between Telescopes and Periscopes, Telescopes and Microscopes, and Telescopes and Kaleidoscopes. However, these statements tell us nothing definite about the relationship between Periscopes, Microscopes, and Kaleidoscopes among themselves.
Evaluating the Syllogism Conclusions
Now, let's check each conclusion against the given statements.
Conclusion I: Some kaleidoscopes are telescopes.
This conclusion is the converse of Statement 3 ("Some telescopes are kaleidoscopes"). As discussed, the converse of a 'Some' statement is always true. If "Some A are B" is true, then "Some B are A" is also true. Since "Some telescopes are kaleidoscopes" is true, it logically follows that "Some kaleidoscopes are telescopes" is also true.
Therefore, Conclusion I follows from the statements.
Conclusion II: Some microscopes are kaleidoscopes.
This conclusion asks about the relationship between Microscopes and Kaleidoscopes. Looking at the statements, we have:
- Some telescopes are microscopes. (Some T are M)
- Some telescopes are kaleidoscopes. (Some T are K)
Both Microscopes and Kaleidoscopes have a 'some' relationship with Telescopes. However, this does not guarantee any relationship between Microscopes and Kaleidoscopes. It is possible to draw Venn diagrams where Some T are M and Some T are K, but there is no overlap between M and K.
For example, consider T = {1, 2, 3, 4, 5}, M = {1, 2}, K = {3, 4}. Here, Some T are M (1, 2 are in both) and Some T are K (3, 4 are in both). But there are no elements common to both M and K, so "Some microscopes are kaleidoscopes" is false in this scenario. Since we can find a scenario where the conclusion is false while the statements are true, this conclusion does not logically follow.
Therefore, Conclusion II does not follow from the statements.
Conclusion III: Some microscopes are telescopes.
This conclusion is the converse of Statement 2 ("Some telescopes are microscopes"). Just like Conclusion I, this conclusion follows directly from the converse rule for 'Some' statements. If "Some A are B" is true, then "Some B are A" is also true. Since "Some telescopes are microscopes" is true, it logically follows that "Some microscopes are telescopes" is also true.
Therefore, Conclusion III follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I follows.
- Conclusion II does not follow.
- Conclusion III follows.
Thus, only conclusions I and III logically follow from the given statements.
Revision Table: Syllogism Rules for 'Some' Statements
| Statement Type | Structure | Converse | Validity | Logical Follows From |
|---|---|---|---|---|
| Particular Affirmative | Some A are B | Some B are A | Always Valid | Statement itself (by conversion) |
| Particular Negative | Some A are not B | Some B are not A | Not Always Valid | None (cannot be simply converted) |
Additional Information: Understanding Syllogism Types
Syllogism is a form of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. In competitive exams, statements and conclusions questions often test your understanding of how different types of statements (like All, No, Some, Some Not) relate to each other.
Key concepts in syllogism include:
- Statements: The given propositions forming the basis of the argument.
- Conclusions: Deductions derived from the statements.
- Quantifiers: Words like 'All', 'No', 'Some', 'Some Not' that specify the quantity of the subject being referred to.
- Terms: The subjects and predicates in the statements and conclusions (e.g., Telescopes, Periscopes, Microscopes, Kaleidoscopes).
- Venn Diagrams: A visual tool using circles to represent sets and their relationships, helpful for analyzing syllogisms.
- Conversion: The process of interchanging the subject and predicate of a statement. The validity of conversion depends on the statement type (e.g., "All A are B" converts to "Some B are A"; "No A are B" converts to "No B are A"; "Some A are B" converts to "Some B are A"; "Some A are not B" cannot be simply converted).
In this problem, understanding the valid conversion of 'Some' statements was crucial. "Some X are Y" always implies "Some Y are X".
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:
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Statements:
Some vehicles are helicopters.
All helicopters are cars.
Conclusions:
I. All vehicles are cars.
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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.
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.
