Syllogism validity check with universal–particular mix: From 'All roads are waters' and 'Some waters are boats', decide which conclusions — (I) 'Some boats are roads' and (II) 'All waters are boats' — follow logically and necessarily.

Given data

• Premise 1: All roads are waters (Roads ⊆ Waters).
• Premise 2: Some waters are boats (∃ Waters ∩ Boats).
• Test: (I) Some boats are roads. (II) All waters are boats.

Concept/Approach

A particular statement about Waters→Boats does not ensure the particular elements are those that are Roads. Also, a universal statement 'All waters are boats' cannot be derived from 'Some waters are boats'.

Step-by-step evaluation

Verification/Alternative

Countermodel: Let Waters = {w1, w2}, Roads = {w1}, Boats = {w2}. Then all premises hold; (I) and (II) are both false. Thus neither conclusion is necessary.

Common pitfalls

• Assuming the 'Some waters are boats' elements lie inside Roads without proof.
• Illicit conversion from 'Some' to 'All'.

Final Answer
Neither I nor II follows.