Set-relation reasoning with overlap: given 'Some dreams are nights' and 'Some nights are days', decide which conclusions necessarily follow (All days are either nights or dreams; Some days are nights)

Given data

• Premise 1: Some Dreams ∩ Nights ≠ ∅.
• Premise 2: Some Nights ∩ Days ≠ ∅.
• Conclusions:
  • I: All Days ⊆ (Nights ∪ Dreams).
  • II: Some Days ∩ Nights ≠ ∅.

Concept/Approach (why this method)

Particular ('some') statements guarantee existence of overlap; they do not justify sweeping universals about entire sets.

Step-by-Step calculation / logic
1) From Premise 2, there exists at least one element that is both Day and Night ⇒ II is necessarily true.2) Nothing links all Days to Nights or Dreams ⇒ I is not compelled and is overgeneralization.

Verification/Alternative

Construct sets where only a small portion of Days overlap Nights; I fails while II holds.

Common pitfalls

• Treating 'some' as 'all'.

Final Answer
Only conclusion II follows.