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Statement — “Rain occurs independently of whether the day is sunny or not. Today, it has rained.”\nQuestion — Which conclusion necessarily follows?

Difficulty: Easy

if only conclusion I follows
if only conclusion II follows
if either I or II follows
if neither I nor II follows, and
None of the above

Correct Answer: if neither I nor II follows, and

Explanation:

Introduction / Context:
The stem explicitly states that rainfall does not depend on whether the day is sunny. It then reports that it rained today. We test whether we can infer sunshine status.

Given Data / Assumptions:
Rain independence: rain may occur on sunny or non-sunny days.

Concept / Approach:
If rain is independent of sunny status, knowing that it rained provides no information about whether the day was sunny. Thus neither “sunny” nor “not sunny” follows.

Step-by-Step Solution:

Conclusion I (“The day is sunny”): Not entailed by rain.Conclusion II (“The day is not sunny”): Also not entailed.

Verification / Alternative check:
Construct two consistent scenarios: (1) a brief sunny interval with a shower; (2) an overcast day with rain. Both satisfy the stem, proving neither I nor II necessarily follows.

Why Other Options Are Wrong:
Any option claiming I or II imposes a dependence the stem denies.

Common Pitfalls:
Assuming “sunny” and “rain” are mutually exclusive; they are not.

Statement — “Rain occurs independently of whether the day is sunny or not. Today, it has rained.”\nQuestion — Which conclusion necessarily follows?

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