Syllogism chain reasoning: given 'Some kings are queens' and 'All queens are beautiful', determine whether it follows that all kings are beautiful or that all queens are kings
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Neither I nor II follows
Explanation
Given data
- Premise 1: Some kings are queens.
- Premise 2: All queens are beautiful.
- Conclusions:
- I: All kings are beautiful.
- II: All queens are kings.
Concept/Approach
From 'Some K are Q' and 'All Q are B', the valid derived conclusion is 'Some kings are beautiful'. However, neither of the provided universal conclusions is justified.
Step-by-step reasoning1) Some K ∩ Q ≠ ∅ and Q ⊆ B → Some K ⊆ B (particular conclusion).2) I (All K ⊆ B) overgeneralizes from 'some' → not valid.3) II (All Q ⊆ K) is converse; not supported.
Verification/Alternative
Countermodel: Let K have members {k1,k2}, Q = {k1}, B contain Q and others. Then 'some K are B' true, I and II false.
Common pitfalls
- Illicit conversion of 'some' to 'all'.
- Assuming symmetry between classes K and Q.
Final AnswerNeither I nor II follows.