In this question, two statements are given, followed by three conclusions labelled I, II and III. You have to consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow(s) from the given statements. Statements: All mansions are palaces. No castles are palaces. Conclusions: I: Some palaces are mansions. II: Some castles are mansions.
Only conclusion I and III follow.
Syllogism Analysis: Statements and Conclusions
This question asks us to analyze two statements and determine which of the given conclusions logically follow from them. We must assume the statements are true, even if they contradict common knowledge. The statements involve the categories: Mansions, Palaces, and Castles.
Understanding the Given Statements
Let's break down the statements provided:
- Statement 1: All mansions are palaces.
- Statement 2: No castles are palaces.
These statements establish relationships between the three categories. Statement 1 tells us that the set of Mansions is a subset of the set of Palaces. Statement 2 tells us that the set of Castles has no members in common with the set of Palaces.
Evaluating Each Conclusion
We will now examine each conclusion based on the relationships established by the statements.
Conclusion I: Some palaces are mansions.
Statement 1 says "All mansions are palaces". If every single mansion is also a palace, then it logically follows that there must be some palaces that are mansions. This is a standard inference in logic: the converse of a universal affirmative ('All A are B') is a particular affirmative ('Some B are A'). As long as there is at least one mansion (which is usually assumed unless specified otherwise), this conclusion holds true.
Therefore, Conclusion I follows from the statements.
Conclusion II: Some castles are mansions.
Statement 2 says "No castles are palaces". This means the sets of Castles and Palaces are completely separate; they have no overlap. Statement 1 says "All mansions are palaces". This means that all mansions are located within the set of Palaces.
If all mansions are inside the set of Palaces, and the set of Castles is completely outside the set of Palaces, then the set of Castles must also be completely outside the set of Mansions. There can be no overlap between Castles and Mansions.
So, the statement "Some castles are mansions" is false based on the given statements.
Therefore, Conclusion II does not follow from the statements.
Conclusion III: No mansions are castles.
Let's revisit the relationships. We know from Statement 1 that all Mansions are within the Palaces set. We know from Statement 2 that the Castles set is entirely separate from the Palaces set.
If Mansions are inside Palaces, and Palaces have no common elements with Castles, then Mansions can also have no common elements with Castles. The statement "No mansions are castles" means that the set of Mansions and the set of Castles are completely separate. This is consistent with our understanding from the statements.
Therefore, Conclusion III follows from the statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I: Some palaces are mansions. (Follows)
- Conclusion II: Some castles are mansions. (Does not follow)
- Conclusion III: No mansions are castles. (Follows)
The conclusions that follow are only Conclusion I and Conclusion III.
| Statement/Conclusion | Relationship Implied | Follows? |
|---|---|---|
| Statement 1: All mansions are palaces. | Mansions <sub>⊂</sub> Palaces | N/A |
| Statement 2: No castles are palaces. | Castles ∩ Palaces = ∅ | N/A |
| Conclusion I: Some palaces are mansions. | Palaces ∩ Mansions ≠ ∅ | Yes (Converse of Statement 1) |
| Conclusion II: Some castles are mansions. | Castles ∩ Mansions ≠ ∅ | No (Contradicted by statements) |
| Conclusion III: No mansions are castles. | Mansions ∩ Castles = ∅ | Yes (Derived from Statements 1 & 2) |
Final Decision
Only Conclusion I and Conclusion III follow from the given statements.
Revision Table: Key Syllogism Rules
| Statement Type | Representation | Converse |
|---|---|---|
| A (All X are Y) | X <sub>⊂</sub> Y | I (Some Y are X) - Simple Converse (valid if X ≠ ∅) |
| E (No X are Y) | X ∩ Y = ∅ | E (No Y are X) - Simple Converse (always valid) |
| I (Some X are Y) | X ∩ Y ≠ ∅ | I (Some Y are X) - Simple Converse (always valid) |
| O (Some X are not Y) | X ∩ Y<sup>c</sup> ≠ ∅ | None (No valid simple converse) |
Additional Information: Syllogism Basics
Syllogisms are 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. The basic structure involves:
- Major Premise: A general statement.
- Minor Premise: A specific statement related to the major premise.
- Conclusion: A statement that follows logically from the two premises.
In the given problem, Statement 1 is the minor premise (containing the subject of the conclusion, "mansions") and Statement 2 is the major premise (containing the predicate of the conclusion, "castles", when conclusion III is considered). The term "palaces" acts as the middle term, connecting the major and minor terms.
Visual tools like Venn diagrams are often helpful in solving syllogism problems. Drawing overlapping or separate circles representing the categories can make the relationships clearer and help verify which conclusions are valid.
Similar Questions
- Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
All water is milk.
No milk is oil.
Conclusions:
(I) Some milk is water.
(II) No oil is water. - Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some vegetables are fruits.
Some fruits are sweets.
Conclusions:
(I) Some fruits are vegetables.
(II) Some sweets are vegetables. - Two statements are given, followed by two conclusions, I and II. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: All bees are hornets.
Statement 2: Some bees are wasps.
Conclusion I: Some hornets are wasps.
Conclusion II: Some wasps are bees. - Two statements are given, followed by three conclusions, I, II and III. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: No boats are ships.
Statement 2: All ship are steamers.
Conclusion I: Some boats are steamers.
Conclusion II: No ships are boats.
Conclusion III: Some steamers are ships. - Given below are two statements, followed by three conclusions, I, II and III. You have to consider the statements to be true even if they seems to be at variance with commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statements.
Statement 1 : All polymers are plastic.
Statement 2 : No rubber is plastic.
Conclusion I : Some polymers are rubber.
Conclusion II : Some plastics are polymer.
Conclusion III : No polymer is rubber. - Given below are two statements, followed by two conclusions, I and II. You have to consider the statements to be true even if they seems to be at variance with commonly known facts. You have to decide which of the given conclusions, if any, follow(s) from the given statements.
Statement 1 : All minutes are seconds.
Statement 2 : No seconds are hours.
Conclusion I : No hours are seconds.
Conclusion II : Some minutes are hours. - Two statements are given, followed by three conclusions, I, II and III. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: No boats are ships.
Statement 2: All ship are steamers.
Conclusion I: Some boats are steamers.
Conclusion II: No ships are boats.
Conclusion III: Some steamers are ships. - Two statements are given, followed by two conclusions, I and II. Consider the statements to be true even if they seem to be at variance with commonly known facts, and decide which of the given conclusions, if any, follow (s) from the given statements.
Statement 1: All bees are hornets.
Statement 2: Some bees are wasps.
Conclusion I: Some hornets are wasps.
Conclusion II: Some wasps are bees. Consider the given statement as true and decide which of the given conclusions can definitely be drawn from the given statements:
Statement:
All rivers are holy. All gods are holy.
Conclusion:
1. All rivers are gods.
2. All gods are rivers.
- Take the given statements to be true and decide which of the conclusions logically follows from the given statements.
Statement: Some ponds are lakes. Some lakes are rivers. Some rivers are seas
Conclusions:
1. Some seas are lakes
2. No sea is a lake
Important Questions from Syllogism
- Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
All water is milk.
No milk is oil.
Conclusions:
(I) Some milk is water.
(II) No oil is water. - Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and decide which conclusion(s) logically follow(s) from the given statements.
Statements:
Some vegetables are fruits.
Some fruits are sweets.
Conclusions:
(I) Some fruits are vegetables.
(II) Some sweets are vegetables. - 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 sparrows are owls.
No sparrow is a parrot.
Conclusions:
(I): No owl is a parrot.
(II): No parrot is a sparrow. 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 forests are hills.
Some hills are deserts.
Conclusions:
(I): All hills are forests.
(II): Some deserts are hills.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 bottles are ludo.
All ludo are dancer.
Conclusions:
(I): Some dancers are ludo.
(II): All bottles are dancers.
