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 crocodiles are tubes.
All tubes are socks.
No sock is a menu.
Conclusions:
(I) Some menus are not socks.
(II) No sock is a crocodile.
(III) Some adapters are houses.
Analyzing the Syllogism: Statements and Conclusions
This problem involves logical reasoning, specifically analyzing syllogisms. We need to determine which conclusions logically follow from the given statements.
Understanding the Statements
Let's break down each statement to understand the relationship between the terms:
- Statement 1: Some crocodiles are tubes. This indicates that there is at least one crocodile that is also a tube. The sets 'crocodiles' and 'tubes' overlap.
- Statement 2: All tubes are socks. This means the entire set of 'tubes' is included within the set of 'socks'. Anything that is a tube is automatically a sock.
- Statement 3: No sock is a menu. This establishes a complete separation between the set of 'socks' and the set of 'menus'. They share no common members. This statement also implies that no menu is a sock.
Combining Information from Statements
By combining the statements, we can infer additional relationships:
- From Statement 1 (Some crocodiles are tubes) and Statement 2 (All tubes are socks), we can logically conclude that some crocodiles are socks. The crocodiles that belong to the 'tubes' category must also belong to the 'socks' category.
- Statement 3 clearly states that the categories 'socks' and 'menus' are mutually exclusive. Using set notation, if $S$ represents the set of socks and $M$ represents the set of menus, then $S \cap M = \emptyset$.
Evaluating the Conclusions
Evaluating Conclusion I: Some menus are not socks
Statement 3 tells us "No sock is a menu", which is logically the same as "No menu is a sock". This means the sets M (menus) and S (socks) are disjoint ($M \cap S = \emptyset$). If no menu is a sock, then any item belonging to the set of menus definitely does not belong to the set of socks. Therefore, assuming the set of menus is not empty (which is standard in these problems), it is true that some menus are not socks. This conclusion logically follows.
Evaluating Conclusion II: No sock is a crocodile
As derived earlier, combining statements 1 and 2 leads to the conclusion that "Some crocodiles are socks". Conclusion II states "No sock is a crocodile". These two statements directly contradict each other. If it's true that some crocodiles are socks, then it cannot be true that no sock is a crocodile. Therefore, Conclusion II does not logically follow.
Evaluating Conclusion III: Some adapters are houses
The terms 'adapters' and 'houses' appear in Conclusion III but are not mentioned in any of the provided statements. Logical conclusions must be based solely on the information given in the statements. Since 'adapters' and 'houses' are unrelated to 'crocodiles', 'tubes', 'socks', or 'menus' within the context of the statements, this conclusion cannot be logically derived. Therefore, Conclusion III does not logically follow.
Final Conclusion
Based on the step-by-step analysis:
- Conclusion I logically follows from the statements.
- Conclusion II does not follow because it contradicts information derived from the statements.
- Conclusion III does not follow because it introduces terms not present in the statements.
Hence, only Conclusion I is a valid deduction.
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.
