Syllogism — Food, sweet, and sour (reading independence of “some”): Statements: • Some food are sweet. • Some food are sour. Conclusions to test: (I) All food are either sweet or sour. (II) Some sweets are sour.

Introduction / Context:This is a classic test of not over-interpreting two particular (“some”) statements. Each premise speaks about a possibly different subset of “food.”

Given Data / Assumptions:

• ∃ (Food ∩ Sweet).
• ∃ (Food ∩ Sour).

Concept / Approach:Because “some” does not mean “all,” the class Food may contain items that are neither sweet nor sour; likewise, the sweet-food items and sour-food items could be entirely different individuals, so there is no guarantee of overlap between Sweet and Sour.

Step-by-Step Evaluation:1) (I) “All food are either sweet or sour” is a universal claim and cannot be inferred from two existential premises.2) (II) “Some sweets are sour” would require a non-empty intersection Sweet ∩ Sour; the premises permit this to be empty because the “some” groups might be disjoint.

Verification / Alternative check:Construct a model with 10 foods: 3 are sweet, 3 are sour, 4 are neither; the premises hold, yet neither (I) nor (II) is forced.

Common Pitfalls:Assuming that two “some” statements imply overlap or exhaustiveness.

Final Answer:Neither Conclusion (I) nor (II) follows.