Statements:\nI. Whenever milk is kept in front of a child, he/she starts crying.\nII. Children cry if they are hungry.\nIII. Unhappy children are hungry.\n\nWhich conclusion logically follows?

Difficulty: Hard

When hungry, a child likes milk.
A child crying means he/she is unhappy.
A happy child does not cry.
An unhappy child usually cries.
None of these

Correct Answer: None of these

Explanation:

Introduction / Context:
This is a logical relations problem. “Whenever milk is kept in front of a child, the child cries” (I) indicates milk-in-front is a sufficient condition for crying. Statement II links hunger to crying (hunger ⇒ crying). Statement III links unhappiness to hunger (unhappy ⇒ hungry ⇒ crying). We must test each conclusion against these implications.

Given Data / Assumptions:

I: milk_in_front ⇒ cry.
II: hungry ⇒ cry.
III: unhappy ⇒ hungry ⇒ cry.

Concept / Approach:
Translate to implications and test converses (which are generally invalid): from A ⇒ B we cannot infer B ⇒ A. None of the conclusions should introduce unstated converses/generalizations.

Step-by-Step Solution:

• (a) “When hungry, a child likes milk.” Hunger ⇒ liking milk is not stated or implied.• (b) “A child crying means unhappy.” We have unhappy ⇒ crying, but not the converse crying ⇒ unhappy; crying could be due to milk being present or other reasons.• (c) “A happy child does not cry.” Not given; a happy child could cry if milk is placed in front (I), or for other reasons.• (d) “An unhappy child usually cries.” III gives unhappy ⇒ hungry ⇒ crying (deterministic), but the option says “usually,” altering modality; though stronger certainty exists in premises, the wording mismatch and lack of “usually” premise makes this not a strict logical follow.

Verification / Alternative check:
Draw implication chain and confirm no converse or added modality sneaks in.

Why Other Options Are Wrong:
They assume converses or add preferences/modalities not in premises.

Common Pitfalls:
Assuming crying implies unhappy; mixing up necessity/sufficiency.

Final Answer:
None of these.

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Statements:\nI. Whenever milk is kept in front of a child, he/she starts crying.\nII. Children cry if they are hungry.\nIII. Unhappy children are hungry.\n\nWhich conclusion logically follows?

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