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 gymnasiums have an electric machine. 2. P is a gymnasium. Conclusions : I. Places other than gymnasium do not have an electric machine.
Only conclusion II follows.
Understanding Logic: Statements and Conclusions Analysis
This question asks us to analyze given statements and determine which of the provided conclusions logically follow from them. We must assume the statements are true, regardless of common knowledge.
Analyzing the Statements
Let's break down the information given in the statements:
- Statement 1: All gymnasiums have an electric machine. This establishes a relationship: If something is a gymnasium, it possesses an electric machine. It does *not* say that only gymnasiums have electric machines.
- Statement 2: P is a gymnasium. This identifies a specific entity, P, and assigns it the property of being a gymnasium.
Analyzing the Conclusions
Now, let's evaluate each conclusion based *only* on the information provided in the statements:
-
Conclusion I: Places other than gymnasium do not have an electric machine.
This conclusion makes a claim about things that are *not* gymnasiums. Statement 1 tells us about gymnasiums (they *do* have electric machines). It provides no information whatsoever about places that are *not* gymnasiums. Such places *might* have electric machines, or they might not. We cannot conclude anything definitive about places other than gymnasiums from the given statements.
Therefore, Conclusion I does not logically follow from the statements.
-
Conclusion II: P has an electric machine.
Statement 2 tells us that P is a gymnasium.
Statement 1 tells us that *all* gymnasiums have an electric machine.
Since P falls into the category of 'gymnasium' (from Statement 2), and every member of this category has an electric machine (from Statement 1), it logically follows that P must have an electric machine.
Therefore, Conclusion II logically follows from the statements.
Final Deduction
Based on our analysis, only Conclusion II can be logically derived from the given statements. Conclusion I makes an assumption about entities not mentioned in the necessary context by the statements.
Thus, only conclusion II follows.
| Item | Based on Statements | Logically Follows? | Reasoning |
|---|---|---|---|
| Statement 1 | All Gymnasiums have Electric Machines | N/A | Given as true |
| Statement 2 | P is a Gymnasium | N/A | Given as true |
| Conclusion I | Places other than Gymnasium do not have Electric Machines | No | Statements provide no info about non-gymnasiums. |
| Conclusion II | P has an Electric Machine | Yes | P is a Gymnasium (Stmt 2) and all Gymnasiums have Electric Machines (Stmt 1). |
Revision Table: Logic Statements and Conclusions
Here's a quick summary of the concepts involved in solving such logic problems:
| Concept | Explanation | Example (from this problem) |
|---|---|---|
| Statement | Given information assumed to be true. | "All gymnasiums have an electric machine." |
| Conclusion | A proposition that must be evaluated for logical validity based on the statements. | "P has an electric machine." |
| Logical Deduction | Deriving a conclusion that is necessarily true if the statements are true. | From "All A are B" and "C is A", concluding "C is B". |
| Inverse Fallacy | Assuming that if "All A are B", then "All non-A are non-B". This is incorrect. | Assuming if "All gymnasiums have electric machines", then "All non-gymnasiums do not have electric machines". |
Additional Information: Syllogism Basics
This question is a simple example of a categorical syllogism. A categorical syllogism is a deductive argument consisting of two premises (statements) and one conclusion. The premises and conclusion are categorical propositions, which assert a relationship between two categories or classes.
Key types of categorical propositions:
- Universal Affirmative (All A are B): Every member of class A is also a member of class B. (e.g., All gymnasiums are places with electric machines).
- Universal Negative (No A are B): No member of class A is a member of class B. (e.g., No gymnasium is a place without an electric machine).
- Particular Affirmative (Some A are B): At least one member of class A is a member of class B. (e.g., Some gymnasiums are large buildings).
- Particular Negative (Some A are not B): At least one member of class A is not a member of class B. (e.g., Some gymnasiums are not air-conditioned).
In our problem, Statement 1 ("All gymnasiums have an electric machine") is a Universal Affirmative proposition. Statement 2 ("P is a gymnasium") identifies a specific instance belonging to the first category. Conclusion II ("P has an electric machine") correctly applies the rule from the universal statement to the specific instance, which is a valid form of deduction (often related to Modus Ponens in propositional logic or universal instantiation in predicate logic).
Important Questions from Statements and Conclusions
In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows the given statements.
Statements:
I. All A are B.
II. Some B are C.
Conclusions:
I. Some A are C.
II. Some A are not C.
III. Some A are B.
Read the given statements and conclusions carefully and decide which of the given conclusions logically follows from the given statements.
Statement:
A asked C, "What time is it now?" Is it half past two? ''
Conclusions:
1. A wants to go to lunch.
2. A wants to confirm what the time is because his watch is off.
In the question one statement is given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement : 55% of Manisha's office colleagues went to watch the movie.
Conclusion I : Manisha went to watch the movie.
Conclusion II : Manisha did not go to watch the movie.
In the question two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.
Statement 1 : All schools are books.
Statement 2 : No books are papers.
Conclusion I : No schools are books.
Conclusion II : Some books are schools.
In the question below are given some statements followed by some conclusions based on those statements. Take the given statements to be true even if they seem to be different from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements.
Statements:
I. Some P are Q.
II. All P are N.
Conclusion:
I. All Q are N.
II. Some P are not Q.
