In this question, a statement is given followed by four conclusions. Choose the conclusion(s) which best fit(s) logically. Statement: To pass the examination, one must work hard. Conclusions: I. Examination is related to only hard work. II. All those who do not work hard pass. III. Without hard work, one does not pass. IV. Hard-working person is a satisfied person.
Only conclusion III follows
Understanding the Logic of the Statement and Conclusions
The question asks us to analyze a given statement and determine which of the four conclusions logically follow from it. The statement provides a condition related to passing an examination and working hard.
Analyzing the Statement: Passing the Examination and Hard Work
The statement is: "To pass the examination, one must work hard."
This statement sets a requirement for passing the examination. It tells us that hard work is a necessary condition for passing the examination. In logical terms, this can be represented as:
\(\text{Pass Examination} \implies \text{Work Hard}\)
This means if someone passes the examination, it necessarily implies they worked hard. It does *not* mean that working hard guarantees passing the examination (hard work is necessary, but not necessarily sufficient).
Evaluating Each Conclusion Based on the Statement
Let's examine each conclusion to see if it logically follows from the statement.
Conclusion I: Examination is related to only hard work.
This conclusion suggests that hard work is the sole factor related to the examination, specifically passing it. The statement says hard work is *necessary* to pass, but it doesn't exclude other factors like understanding the subject, preparing effectively, having a good teacher, or even external factors. The phrase "only hard work" is too restrictive and is not supported by the statement, which only specifies one necessary condition.
Therefore, Conclusion I does not logically follow.
Conclusion II: All those who do not work hard pass.
This conclusion is the opposite of what the statement implies. If someone does *not* work hard, according to the statement (\(\text{Pass Examination} \implies \text{Work Hard}\)), they cannot pass the examination. The logical contrapositive of the statement is \(\text{Not Work Hard} \implies \text{Not Pass Examination}\). This means if you don't work hard, you don't pass.
Therefore, Conclusion II does not logically follow; in fact, it contradicts the statement.
Conclusion III: Without hard work, one does not pass.
This conclusion states that if someone does not work hard, they will not pass the examination. This is the contrapositive of the original statement (\(\text{Pass Examination} \implies \text{Work Hard}\)). The contrapositive of a conditional statement is logically equivalent to the original statement. If passing requires hard work, then not working hard means not passing.
Therefore, Conclusion III logically follows from the statement.
Conclusion IV: Hard-working person is a satisfied person.
The statement only discusses the relationship between passing an examination and working hard. It makes no mention of satisfaction or the emotional state of a hard-working person. We cannot infer anything about satisfaction from the given statement.
Therefore, Conclusion IV does not logically follow.
Summary of Logical Conclusions
Based on our analysis:
- Conclusion I: Does NOT follow.
- Conclusion II: Does NOT follow.
- Conclusion III: Does follow.
- Conclusion IV: Does NOT follow.
Thus, only Conclusion III logically follows from the given statement.
| Conclusion | Logical Analysis | Follows? |
|---|---|---|
| I. Examination is related to only hard work. | Statement says hard work is necessary for passing, not the only factor. | No |
| II. All those who do not work hard pass. | Directly contradicts the statement's contrapositive (Not work hard implies not pass). | No |
| III. Without hard work, one does not pass. | This is the contrapositive of the statement (Pass implies Work Hard is equivalent to Not Work Hard implies Not Pass). | Yes |
| IV. Hard-working person is a satisfied person. | The statement provides no information about satisfaction. | No |
Therefore, the only conclusion that logically fits is Conclusion III.
Revision Table: Key Concepts in Logical Reasoning
| Concept | Explanation | Relevance to Question |
|---|---|---|
| Conditional Statement | A statement in the form "If P, then Q". Denoted as \(P \implies Q\). P is the antecedent, Q is the consequent. | The statement "To pass the examination, one must work hard" can be interpreted as "If one passes the examination, then one works hard." |
| Necessary Condition | Q is a necessary condition for P if P cannot be true unless Q is true (\(P \implies Q\)). | Hard work is a necessary condition for passing the examination according to the statement. |
| Sufficient Condition | P is a sufficient condition for Q if P's truth guarantees Q's truth (\(P \implies Q\)). | The statement does NOT say hard work is sufficient for passing. Working hard might not guarantee a pass. |
| Contrapositive | The statement "If not Q, then not P". Denoted as \(\neg Q \implies \neg P\). Logically equivalent to the original statement \(P \implies Q\). | The contrapositive of "If pass, then work hard" is "If not work hard, then not pass," which is Conclusion III. |
| Logical Inference | Drawing conclusions that are guaranteed to be true if the premises (statement) are true. | We must only accept conclusions that are strictly supported by the statement, without adding outside information or assumptions. |
Additional Information: Avoiding Common Logical Fallacies
When dealing with logical reasoning questions, it's important to avoid common errors in thinking:
- Affirming the Consequent: Assuming \(P\) is true just because \(Q\) is true, based on \(P \implies Q\). (e.g., Assuming someone passed *because* they worked hard - the statement only says if they passed, they must have worked hard, not the reverse).
- Denying the Antecedent: Assuming \(\neg Q\) is true just because \(\neg P\) is true, based on \(P \implies Q\). (e.g., Assuming someone didn't work hard *because* they didn't pass - the statement says if they didn't work hard, they didn't pass, but someone might not pass for other reasons even if they worked hard).
- Introducing Outside Information: Bringing in general knowledge or assumptions that are not explicitly stated in the premise. (e.g., Assuming hard-working people are satisfied, or assuming examinations are *only* about hard work).
In this question, Conclusion I makes the mistake of assuming "only hard work," adding outside information. Conclusion II denies the contrapositive. Conclusion IV introduces unrelated information about satisfaction. Only Conclusion III correctly identifies the logical contrapositive of the statement.
Important Questions from Statements and Conclusions
A situation is given, followed by two conclusions I and II. Read the situation and both the conclusions carefully and select the correct answer.
Situation:
Since the past 15 years, 75% of the products in the world’s pottery market comes from Country K. However, the employment in the pottery industry of Country K has been consistently declining by 5-9% every year since the past 3 years.
Conclusions:
I. Even after declining employment, Country K has enough potters to continue contributing equally to the international market.
II. The local demand of pottery in Country K has substantially decreased leading to less interest among potters.
The statement below is followed by three conclusions labelled I, II and III. You have to assume everything in the statement to be true, and then decide which of the three suggested conclusions logically follows for pursuing.
Statements:
1) No school is an institution but they are establishment.
2) All establishments that are not institutions have buildings.
Conclusions:
I. Schools are not establishments.
II. All schools have buildings.
III. Schools do not have buildings.Read the given statements and conclusion carefully and decide which of the following options is true with respect to the given conclusion.
Statements:
The Gateway of India is in Mumbai.
Mumbai is in India.
Conclusion:
The Gateway of India is in India.
Read the given statements and conclusion carefully and decide which of the following options is true with respect to the given conclusion.
Statements:
Men who are handsome are generally of the intellectual type.
Vikram is handsome.
Conclusion:
Vikram is intellectual.Given is a statement, followed by four conclusions. Read the statement carefully and decide which of the conclusions logically follow(s) from the given statement.
Statement:
This book can help because all good books help.
Conclusions:
I. This is not a good book.
II. This is a good book.
III. No good book helps.
IV. Some good books help.
