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)
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Only conclusion II follows
Explanation
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 / logic1) 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 AnswerOnly conclusion II follows.