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Logical Deduction – Identify the statement that is logically equivalent to the given rule Rule: To pass the examination, one must work hard.

Difficulty: Easy

Correct Answer: Without hard work, one does not pass the examination.

Explanation:


Introduction / Context:
This verbal reasoning item tests your understanding of necessary conditions. The statement “To pass the examination, one must work hard” sets up a necessity: hard work is required for passing. The task is to find the option that is logically equivalent to this necessity.


Given Data / Assumptions:

  • Original rule: Passing requires hard work.
  • We assume no hidden sufficiency claims (that hard work alone guarantees passing).
  • We seek an equivalent restatement using standard logic.


Concept / Approach:
In logic, “A requires B” means “If A, then B.” The contrapositive, which is logically equivalent, is “If not B, then not A.” Here, A = pass; B = work hard. So the contrapositive is “If one does not work hard, then one does not pass.”


Step-by-Step Solution:

Let P = “pass the examination,” H = “work hard.”Given: P -> H (passing implies hard work is present).Contrapositive: not H -> not P (absence of hard work implies not passing).Option D states exactly this contrapositive.


Verification / Alternative check:

Check that option D preserves necessity but does not falsely add sufficiency. It does: it says lack of H prevents P, which matches the original rule’s force.


Why Other Options Are Wrong:

A: Too vague; it does not encode necessity.B: States sufficiency (hard work guarantees passing), which is stronger than the given rule.C and E: Irrelevant sentiments; they do not capture the logical structure.


Common Pitfalls:

Confusing “necessary” with “sufficient.” The statement does not claim that working hard ensures passing, only that it is required.


Final Answer:
Without hard work, one does not pass the examination.

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