Mixed particular and universal with attribute layering: Using 'Some swords are sharp' and 'All swords are rusty', test whether the conclusions (I) 'Some rusty things are sharp' and (II) 'Some rusty things are not sharp' must be true.

Given data

• Premise 1: Some Swords are Sharp (∃ Sword ∩ Sharp).
• Premise 2: All Swords are Rusty (Sword ⊆ Rusty).
• Conclusions: (I) Some Rusty things are Sharp. (II) Some Rusty things are not Sharp.

Concept/Approach

Map attributes: If a subset (Swords) lies entirely within Rusty, then any particular Sword (sharp or not) is a Rusty thing. From 'Some Swords are Sharp' it follows that some Rusty things (those sharp swords) are Sharp. But we cannot assert existence of non-sharp swords.

Step-by-step evaluation

Verification/Alternative

Countermodel for (II): Let all Swords be Sharp; both premises hold, but there is no Rusty ∧ ¬Sharp element. Hence (II) is not necessary.

Common pitfalls

• Assuming from 'Some swords are sharp' that some swords are not sharp; such a negation is unwarranted.

Final Answer
Only conclusion I follows.