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
- In this question, three 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 follows/follow from the statements.
Statements:
I. Some tables are chairs.
II. All desks are chairs.
III. No chair is a fan.
Conclusions:
I. Some desks are tables.
II. Some fans are desks. - In this question, three 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 follows/follow from the statements.
Statements:
I. All tables are charts.
II. Some charts are graphs.
III. Some graphs are pies.
Conclusions:
I. No table is a graph.
II. Some pies are charts. - In this question, three 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 follows/follow from the statements.
Statements:
All boxes are squares.
All squares are rectangles.
All rectangles are figures.
Conclusions:
I. All boxes are figures.
II. All squares are figures. Three 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 given conclusions logically follow(s) from the statements.
Statements:
Some fractions are marts.
No mart is a stud.
All studs are frogs.
Conclusions:
I. Some fractions are definitely not studs.
II. Some fractions are definitely not marts.
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:
Some calculators are lanterns.
Some lanterns are mobiles.
Conclusions:
I. All mobiles are calculators.
II. No mobile is a lantern.
III. Some mobiles are lanterns.
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 parrots are crows.
All crows are eagles.
Conclusions:
I. All parrots are eagles.
Il. Some crows are parrots.
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 from the statements.
Statements:
No certificate is a paper.
All pens are papers.
Conclusions:
I. No certificate is a pen.
II. No paper is a certificate.
III. Some papers are pens.
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:
Some officers are clerks.
All clerks are workers.
Conclusions:
I. Some workers are officers.
Il. No worker is an officer.
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 chargers are phones.
No phone is a watch.
Conclusions:
I. All phones are chargers.
Il. No charger is a watch.
Ill. No watch is a phone.
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 wallets are bags.
Some bags are envelopes.
Conclusions:
I. Some wallets are envelopes.
II. No wallet is an envelope.
III. No bag is an envelope.
Important Questions from Syllogism
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:
Some students are players.
All players are male.
Conclusions:
I. All males are players.
II. Some males are students.
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:
No creative is an employer.
All experts are creative.
All workers are experts.
Conclusions:
I. No employer is an expert.
II. No worker is an employer.
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:
Some actors are choreographers.
All choreographers are producers.
Not a single producer is a director.
Conclusions:
I. Some actors are directors.
II. Not a single actor is a director.
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 :
1. All flowers are tulips.
2. No tulips are whites.
Conclusions :
I. All tulips are flowers.
II. Some tulips are whites.
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 rats are dogs.
Some rats are hens.
Conclusions:
I. Some rats are dogs.
II. Some hens are rats.
