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.
Understanding Logical Reasoning: Statements and Conclusions
Logical reasoning problems involving statements and conclusions test your ability to deduce information based purely on the given premises, even if they contradict common knowledge. We are given two statements and three conclusions, and we need to determine which conclusions logically follow from the statements.
Analyzing the Statements
Let's break down the given statements:
- Statement 1: All chargers are phones.
- Statement 2: No phone is a watch.
These statements establish a relationship between three categories: Chargers, Phones, and Watches. Statement 1 tells us that the set of 'Chargers' is completely included within the set of 'Phones'. Statement 2 tells us that the sets of 'Phones' and 'Watches' are completely separate; they have no elements in common.
Analyzing the Conclusions
Now let's examine each conclusion based on the truth of the statements:
- Conclusion I: All phones are chargers.
- Conclusion II: No charger is a watch.
- Conclusion III: No watch is a phone.
Step-by-Step Evaluation of Conclusions
Evaluating Conclusion I: All phones are chargers
Statement 1 says, "All chargers are phones". This means that if something is a charger, it must also be a phone. However, it does not necessarily mean that everything that is a phone is also a charger. The set of phones could be larger than the set of chargers, with some phones not being chargers. For example, if there are 10 phones and 5 of them are chargers, then all 5 chargers are phones, but it's not true that all 10 phones are chargers.
In logical terms, the statement "All A are B" does not imply "All B are A". The converse is not necessarily true.
Therefore, Conclusion I does not logically follow from the given statements.
Evaluating Conclusion II: No charger is a watch
We know from Statement 1 that all chargers are phones (Chargers <span>⊆</span> Phones). We also know from Statement 2 that no phone is a watch (Phones <span>∩</span> Watches <span>=</span> <span>∅</span>). Since the set of chargers is entirely contained within the set of phones, and the set of phones has no overlap with the set of watches, it logically follows that the set of chargers can also have no overlap with the set of watches.
If every charger is a phone, and no phone is a watch, then nothing that is a charger can be a watch.
Therefore, Conclusion II logically follows from the given statements.
Evaluating Conclusion III: No watch is a phone
Statement 2 says, "No phone is a watch". This establishes a mutual exclusion between the sets of phones and watches. If something is a phone, it cannot be a watch. Similarly, if something is a watch, it cannot be a phone.
In logical terms, the statement "No A is B" is equivalent to the statement "No B is A". The converse is logically equivalent for E-type (No S is P) categorical propositions.
Therefore, Conclusion III logically follows from the given statements.
Summary of Conclusions
Based on our analysis:
- Conclusion I: All phones are chargers - Does not follow.
- Conclusion II: No charger is a watch - Follows.
- Conclusion III: No watch is a phone - Follows.
Thus, only conclusions II and III logically follow from the given statements.
| Statement/Conclusion | Relation | Follows? |
|---|---|---|
| Statement 1 | All Chargers are Phones | Given |
| Statement 2 | No Phone is a Watch | Given |
| Conclusion I | All Phones are Chargers | No (Converse of Stmt 1) |
| Conclusion II | No Charger is a Watch | Yes (From Stmt 1 & 2) |
| Conclusion III | No Watch is a Phone | Yes (Converse of Stmt 2) |
Final Answer Deduction
The conclusions that follow are Conclusion II and Conclusion III. We look for the option that states this.
The correct option is the one that says "Only conclusions II and III follow".
Revision Table: Key Logical Concepts
| Concept | Explanation | Example |
|---|---|---|
| Categorical Proposition | A statement that relates two categories (or terms). | All A are B, No A is B, Some A are B, Some A are not B. |
| Universal Affirmative (A) | All S are P. Subject is included in Predicate. | All dogs are mammals. |
| Universal Negative (E) | No S is P. Subject and Predicate are mutually exclusive. | No fish are birds. |
| Converse | Swapping the subject and predicate terms of a proposition. | Converse of "All A are B" is "All B are A". Converse of "No A is B" is "No B is A". |
| Logical Consequence | A conclusion that must be true if the premises (statements) are true. | If All A are B and All B are C, then All A are C. |
Additional Information: Venn Diagrams in Syllogisms
Venn diagrams are a helpful visual tool for solving syllogism problems like this one. Each category is represented by a circle, and the relationships between categories are shown by the overlap or separation of the circles.
- "All chargers are phones": Draw a circle for 'Chargers' entirely inside a circle for 'Phones'.
- "No phone is a watch": Draw a circle for 'Watches' completely separate from the 'Phones' circle.
Based on this diagram, the 'Chargers' circle is inside the 'Phones' circle, and the 'Phones' circle is separate from the 'Watches' circle. This clearly shows that the 'Chargers' circle must also be separate from the 'Watches' circle. This supports the conclusion "No charger is a watch". It also shows that the 'Watches' circle is separate from the 'Phones' circle, supporting "No watch is a phone". Finally, since the 'Chargers' circle is only *part* of the 'Phones' circle (unless stated otherwise), you can see that not all items in the 'Phones' circle are necessarily in the 'Chargers' circle, thus "All phones are chargers" does not necessarily follow.
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.
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.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:
Some boys are brave.
All boys are punctual.
Conclusions:
I. Some brave are boys.
II. Some punctual are boys.
III. Some brave are punctual.
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.
