Syllogism with universal and negative premises: From 'All roads are poles' and 'No pole is a house', decide whether the conclusions (I) 'Some roads are houses' and (II) 'Some houses are poles' can be affirmed as logically necessary.
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Neither I nor II follows
Explanation
Given data
- Premise 1: Roads ⊆ Poles.
- Premise 2: Poles ∩ Houses = ∅.
- Conclusions: (I) Some Roads are Houses. (II) Some Houses are Poles.
Concept/Approach
If no Pole is a House, then any subset of Poles (including Roads) has empty intersection with Houses. Particular claims asserting such intersections are false.
Step-by-step evaluation
1) From Premise 2, Poles and Houses are disjoint.2) Since Roads ⊆ Poles, Roads ∩ Houses = ∅ ⇒ (I) cannot hold.3) Directly, 'Some Houses are Poles' contradicts Premise 2 ⇒ (II) cannot hold.Verification
Venn diagram readily shows disjointness between Poles and Houses, eliminating both conclusions.
Common pitfalls
- Overlooking that a subset (Roads) inherits disjointness from its superset (Poles).
Final AnswerNeither I nor II follows.