Syllogism — Premises: All fruits are sweet. All sweet things are not good for health (i.e., no sweet thing is good for health). Conclusions: (I) All fruits are not good for health. (II) Some fruits are not good for health.

Introduction / Context:
The phrase 'All sweet things are not good for health' is read in reasoning tests as 'No sweet thing is good for health' (a universal negative). Combined with 'All fruits are sweet', we test the two conclusions.

Given Data / Assumptions:

• Fruits ⊆ Sweet.
• Sweet ⊆ NotGoodForHealth (equivalently, Sweet ∩ GoodForHealth = ∅).
• Fruits is a non-empty everyday category.

Concept / Approach:
By transitivity, Fruits ⊆ NotGoodForHealth, validating (I). If any fruit exists, then at least one fruit is not good for health, validating (II) as an existential consequence.

Step-by-Step Solution:

Verification / Alternative check:
Venn diagram confirms Fruits entirely lies within NotGoodForHealth, ensuring both universal and existential claims.

Why Other Options Are Wrong:
Any option denying either (I) or (II) conflicts with the derived inclusion and routine existential assumption.

Common Pitfalls:
Misreading 'all ... are not' as 'not all ... are', which is different in logic.

Final Answer:
Both (I) and (II) follow.