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.
Verbal Reasoning
Logical Deduction
Difficulty: Medium
Choose an option
Answer
Correct Answer: Neither I nor II follows
Explanation
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
1) Roads are a subset of Waters.2) At least one Water is a Boat; this could be a water element that is not a Road.3) Hence (I) 'Some boats are roads' is not forced; may be false in some models.4) (II) upgrades 'Some' to 'All' — an invalid generalization.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 AnswerNeither I nor II follows.