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 chart is a casket.
Not a single casket is a house.
Every house is an adapter.
Conclusions:
(I) Some adapters which are houses are charts as well.
(II) No chart is a house.
(III) Some adapters are houses.
Statements: Chart, Casket, House Relationships
The task is to determine which conclusions logically follow from the given statements. We must assume the statements are true, irrespective of whether they align with common knowledge.
Premises: Chart, Casket, House Logic
Let's break down the relationships described in the premises using set theory notation for clarity:
- Statement 1: No chart is a casket.
Formal Logic: This means the set of Charts (C) and the set of Caskets (K) have no common elements. Represented as: $C \cap K = \emptyset$. - Statement 2: Not a single casket is a house.
Formal Logic: Similarly, the set of Caskets (K) and the set of Houses (H) are disjoint. Represented as: $K \cap H = \emptyset$. - Statement 3: Every house is an adapter.
Formal Logic: This means the entire set of Houses (H) is contained within the set of Adapters (A). Represented as: $H \subseteq A$.
Conclusions: Evaluating Chart, House Links
We will now systematically evaluate each conclusion based on the logical implications of the premises.
Conclusion I: Adapters, Houses, Charts Link
Claim: Some adapters which are houses are charts as well.
Meaning: Since Statement 3 establishes that all Houses are Adapters ($H \subseteq A$), the phrase 'adapters which are houses' simply refers to the set of Houses (H). Therefore, this conclusion claims that there is an overlap between the set of Houses (H) and the set of Charts (C). In set notation: $H \cap C \neq \emptyset$.
Analysis: From Statement 1 ($C \cap K = \emptyset$) and Statement 2 ($K \cap H = \emptyset$), we know that both Charts and Houses are separate from Caskets. However, these statements do not provide any information linking Charts and Houses directly or indirectly. It is possible for them to overlap, or to be completely separate.
Example Scenario: Consider Charts = {1}, Caskets = {2}, Houses = {3}, and Adapters = {3, 4}. Here, Statement 1 ($ \{1\} \cap \{2\} = \emptyset $) and Statement 2 ($ \{2\} \cap \{3\} = \emptyset $) are true. Statement 3 ($ \{3\} \subseteq \{3, 4\} $) is also true. However, Conclusion I ($H \cap C \neq \emptyset$) is false because $ \{3\} \cap \{1\} = \emptyset $. Since we can find a valid case where the conclusion is false, it does not logically follow.
Verdict: Conclusion I does not follow.
Conclusion II: Chart House Disjoint Check
Claim: No chart is a house.
Meaning: This conclusion asserts that the set of Charts (C) and the set of Houses (H) have no members in common. In set notation: $C \cap H = \emptyset$.
Analysis: Just like with Conclusion I, the premises $C \cap K = \emptyset$ and $K \cap H = \emptyset$ do not logically necessitate that $C \cap H = \emptyset$. The separation from Caskets does not imply separation between Charts and Houses.
Example Scenario: Let Charts = {1, 2}, Caskets = {3, 4}, Houses = {1, 5}, and Adapters = {1, 5, 6}. The statements hold: No {1, 2} is {3, 4}. No {3, 4} is {1, 5}. Every {1, 5} is in {1, 5, 6}. However, Conclusion II ($C \cap H = \emptyset$) is false because the element '1' exists in both the Charts set and the Houses set.
Verdict: Conclusion II does not follow.
Conclusion III: Adapter House Overlap Check
Claim: Some adapters are houses.
Meaning: This conclusion states that there is at least one element that belongs to both the set of Adapters (A) and the set of Houses (H). In set notation: $A \cap H \neq \emptyset$.
Analysis: Statement 3 directly states $H \subseteq A$. This means every element in H is also in A. Assuming the set of Houses is not empty (which is a standard assumption in such logic problems unless specified otherwise), there must be at least one house. Because every house is an adapter, this existing house is also an adapter. Therefore, the intersection of Adapters and Houses ($A \cap H$) is precisely the set of Houses (H), which we assume is non-empty. Hence, $A \cap H \neq \emptyset$.
Verdict: Conclusion III follows.
Deduction: Final Conclusion Validity
After analyzing each conclusion against the given statements:
- Conclusion I does not logically follow.
- Conclusion II does not logically follow.
- Conclusion III logically follows.
Therefore, the only conclusion that is logically guaranteed by the premises is Conclusion III.
Similar Questions
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:
No book is a novel.
All novels are diaries.
Conclusions:
I. All diaries can never be books.
II. Some books are diaries.
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 rhombuses are tangents.
All chords are tangents.
Conclusions:
I. Some rhombuses being chords is a possibility.
II. Some tangents are rhombuses.
Three statements are followed by three conclusions numbered I, II, 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 follows from the given statements.
Statements :
No Mango is a banana.
No banana is a guava.
Some guavas are oranges.
Conclusions :
(I) Some mangoes are oranges.
(II) Some guavas are mangoes.
(III) No orange is a banana.
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 tigers are fishes.
No elephant is a tiger.
Some deer are tigers.
Conclusions:
I. Some fishes are deer.
II. No elephant is a deer.
III. No deer is a fish.
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.
Statement :
All Bananas are Grapes.
All Papayas are Pineapple.
Some Pineapples are Banana.
Conclusions:
(I) Some Papayas are Grapes.
(II) Some Grapes are Pineapples.
(III) Some Bananas are Papayas.
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 defects are problems.
Some problems are solutions.
Conclusions:
I. Some defects being solutions is a possibility.
II. No solution is a defect.
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:
Some bags are sacks.
Some sacks are juts.
Conclusions:
I. Some bags are juts.
II. Some juts are sacks.
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 boxes are pins.
All pins are taps.
No tap is a star.
Conclusions:
I. All boxes are pins.
II. Some taps are pins.
III. Some stars are not taps.
Two statements are given, followed by two conclusions numbered I and II. Taking the statements to be true, even if they seem to be at variance from commonly known facts, decide which of the conclusions logically follows from the statements.
Statements:
All cycles are buses.
Some buses are trains.
Conclusions:
I. No cycle is train.
II. All cycles are trains.
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.
Statement:
Some figs are orange.
All oranges are grapes.
All mangoes are oranges.
Conclusions:
(I) Some figs are grapes.
(II) All mangoes are grapes.
(III) Some mangoes are figs.
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.
