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 phones are keyboards. All phones are computers. Conclusions: I. Some keyboards are computers. II. Some computers are phones.
Only Conclusion I and II follows
Understanding Statements and Conclusions Logic
This type of question tests your ability to draw logical conclusions based on given statements, regardless of whether the statements align with real-world facts. We need to determine which of the provided conclusions logically follow from the given statements.
Let's analyze the given statements:
- Some phones are keyboards.
- All phones are computers.
Analyzing the Statements using Venn Diagrams
We can use Venn diagrams to visualize the relationships described in the statements.
- Statement 1: "Some phones are keyboards" means there is an overlap between the set of Phones and the set of Keyboards.
- Statement 2: "All phones are computers" means the entire set of Phones is included within the set of Computers. The circle representing Phones is completely inside the circle representing Computers.
Combining these two statements:
Since all phones are computers (Statement 2), the area where Phones overlap with Keyboards (from Statement 1) must also be inside the set of Computers. This means there is an overlap between the set of Keyboards and the set of Computers.
Evaluating the Conclusions Based on Statements
Conclusion I: Some keyboards are computers.
Based on our analysis:
- Statement 1: Some Phones are Keyboards.
- Statement 2: All Phones are Computers.
If some items in the 'Phones' category are also in the 'Keyboards' category, and every item in the 'Phones' category is also in the 'Computers' category, then those specific phones that are keyboards must also be computers. This establishes a relationship between Keyboards and Computers, where some part of Keyboards is also part of Computers.
Therefore, the conclusion "Some keyboards are computers" logically follows from the statements.
Conclusion II: Some computers are phones.
Let's look at Statement 2 again: "All phones are computers".
This statement tells us that the set of Phones is a subset of the set of Computers. If set A is entirely contained within set B (All A are B), it logically follows that some elements of set B must be elements of set A (Some B are A).
Since all phones are computers, it means the group of computers includes all phones. Thus, some computers are definitely phones.
Therefore, the conclusion "Some computers are phones" logically follows from the statements.
Conclusion III: No keyboard is computer.
We have already established that Conclusion I, "Some keyboards are computers", is true based on the given statements. Conclusion III, "No keyboard is computer", is the direct opposite (contradictory) of Conclusion I.
If it is true that "Some keyboards are computers", then it cannot be true that "No keyboard is computer".
Therefore, the conclusion "No keyboard is computer" does not logically follow from the statements.
Summary of Logical Conclusions
Based on the analysis, the conclusions that logically follow from the given statements are:
- Conclusion I: Some keyboards are computers. (Follows)
- Conclusion II: Some computers are phones. (Follows)
- Conclusion III: No keyboard is computer. (Does not follow)
Thus, only Conclusion I and Conclusion II follow.
Matching with Given Options
We need to find the option that states "Only Conclusion I and II follows".
- Option 1: Only conclusion II follows (Incorrect)
- Option 2: Only Conclusion I and II follows (Correct)
- Option 3: Only conclusion I follows (Incorrect)
- Option 4: Either Conclusion I or III follows (Incorrect, as I definitely follows and III does not)
The option that matches our derived result is Option 2.
Revision Table: Types of Statements in Syllogism
| Type of Statement | Structure | Quantifier | Quality | Example |
|---|---|---|---|---|
| Universal Affirmative (A) | All A are B | All | Affirmative | All cats are animals. |
| Universal Negative (E) | No A is B | No | Negative | No dog is a cat. |
| Particular Affirmative (I) | Some A are B | Some | Affirmative | Some birds are black. |
| Particular Negative (O) | Some A are not B | Some | Negative | Some birds are not black. |
Additional Information: Solving Syllogism Problems
Syllogism is a form of logical reasoning where a conclusion is derived from two or more statements (premises). Mastering syllogism questions is crucial for competitive exams.
Common methods to solve syllogism problems include:
- Venn Diagrams: Drawing overlapping or contained circles to represent the sets mentioned in the statements. This visual method helps in understanding the relationships and checking if a conclusion holds true in all possible diagrams.
- Analytical Method/Rules: Using a set of rules regarding the middle term, distribution of terms, and quality/quantity of statements and conclusions. This method requires understanding concepts like 'distribution' of terms in a statement.
In this problem, using Venn diagrams makes it clear how the sets of Phones, Keyboards, and Computers relate, leading directly to the valid conclusions.
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:
All dancers are talented.
Some girls are dancers.
Conclusions:
I. Some girls are talented.
II. All talented are girls.
III. All girls are talented.
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 directors are actors.
No actor is a producer.
All choreographers are directors.
Conclusions:
I. No choreographer is producer.
II. Some actors are choreographers.
III. No director is a producer.
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 follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
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 cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
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 employees are tax-payers.
Some employees are farmers.
Some farmers are doctors.
Conclusions:
I. No farmer is a tax-payer.
II. Some farmers are tax-payers.
