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:
1) All clothes are black.
2) All shirts are clothes.
Conclusions:
I. All shirts are black.
II. Some clothes are black.
Logical Reasoning: Analyzing Syllogism Statements
This problem tests logical deduction skills using syllogisms. We are given two statements that we must assume are true, even if they contradict real-world facts. Our task is to determine which of the two conclusions logically follows from these statements.
Statement Breakdown and Analysis
Let's break down the given statements:
- Statement 1: All clothes are black.
- This means that the set of all items considered 'clothes' is entirely included within the set of 'black' things.
- If we represent 'clothes' as set C and 'black things' as set B, then Statement 1 means that C is a subset of B ($C \subseteq B$).
- Statement 2: All shirts are clothes.
- This means that the set of all items considered 'shirts' is entirely included within the set of 'clothes'.
- If we represent 'shirts' as set S, then Statement 2 means that S is a subset of C ($S \subseteq C$).
Evaluating Conclusion I: All shirts are black
We need to determine if the statement "All shirts are black" logically follows.
- From Statement 2, we have $S \subseteq C$ (All shirts are clothes).
- From Statement 1, we have $C \subseteq B$ (All clothes are black).
- Using the property of transitivity in sets, if the set S is contained within C, and C is contained within B, then S must be contained within B.
- Mathematically, if $S \subseteq C$ and $C \subseteq B$, then $S \subseteq B$.
- This directly translates to "All shirts are black".
- Therefore, Conclusion I logically follows from the statements.
Evaluating Conclusion II: Some clothes are black
Next, let's evaluate the conclusion "Some clothes are black".
- Statement 1 says "All clothes are black" ($C \subseteq B$).
- This is a universal affirmative statement. In standard logic, universal statements (like "All A are B") imply the existence of members in the subject class (A, which is 'clothes' here).
- Given that "All clothes are black" is true, it implies that the category 'clothes' is not empty and every item in this category is black.
- If every single cloth is black, it necessarily means that at least some clothes are black.
- Therefore, Conclusion II also logically follows from Statement 1.
Determining the Final Answer
Our analysis shows that both conclusions are logically sound based on the given statements:
- Conclusion I ("All shirts are black") follows.
- Conclusion II ("Some clothes are black") follows.
Since both conclusions are valid, the option stating that both conclusions follow is the correct one.
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.
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.
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 shoes are slippers.
All slippers are socks.
All socks are sandals
Conclusions:
(I) Some sandals are slippers
(II) Some socks are shoes.
(III) All sandals are shoes.
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.
