Question

Consider the following statement choose the correct answer which logically follows from the given statement:
Statement: To pass the examination, one must work hard.

• A. Examination is related with hard work.
• B. All those who work hard, pass.
• C. Examination causes some anxiety and those who work hard, overcome it.
• D. Without hard work, one doesn’t pass.

Hint:

The contrapositive is always logically equivalent to the original statement:
- Statement: If \(P\), then \(Q\).
- Contrapositive: If not \(Q\), then not \(P\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question evaluates logical deduction and conditional reasoning.
A conditional statement can be represented symbolically as:
\[ P \implies Q \] where \(P\) is a sufficient condition for \(Q\), and \(Q\) is a necessary condition for \(P\).
Detailed Explanation:
Let us translate the given statement into logical terms:
- "To pass the examination, one must work hard."
This means that passing the examination (\(P\)) requires working hard (\(W\)).
Thus, working hard is a necessary condition for passing the examination.
Symbolic representation:
\[ P \implies W \] Let us evaluate the options using formal logic rules:
- Option (B): "All those who work hard, pass."
This translates to \(W \implies P\) (treating hard work as a sufficient condition). This is a logical fallacy known as the converse error, as working hard is necessary but may not be sufficient on its own to guarantee a pass.
- Option (C): Introduces external concepts (such as "anxiety") that are not mentioned in the original statement.
- Option (D): "Without hard work, one doesn't pass."
This translates to \(\neg W \implies \neg P\).
According to the rule of transposition in formal logic, a conditional statement is logically equivalent to its contrapositive:
\[ (P \implies W) \equiv (\neg W \implies \neg P) \] Therefore, "Without hard work, one doesn't pass" is the contrapositive and is logically equivalent to the original statement.

Step 2: Final Answer:
The statement that logically follows is Option (D).