Concept:Analyze all possible seating arrangements on a circular table with five equidistant chairs to check which statements must always be true.
Explanation:Place A at position 1 on a circle of five positions numbered 1–5 in order.
From I: C is next to A → C can be at position 2 or 5.
From II: A is two seats from D → D is at position 3 or 4 (exactly one seat between them).
From III: B is not next to A → B cannot be at 2 or 5.
Consider each case for C:
• If C is at 2: A=1, C=2. D ∈ {3,4}, B ∈ {3,4} but B ≠5. In both subcases (D=3,B=4 or D=4,B=3), D and B are adjacent, and the remaining person E automatically sits at 5, which is adjacent to A. So both I and II are true.
• If C is at 5: A=1, C=5. D ∈ {3,4}, B ∈ {3,4} but B ≠2. In both subcases (D=3,B=4 or D=4,B=3), D and B are adjacent, and E sits at 2, which is adjacent to A. Again both I and II are true.
Thus in every valid arrangement, D is next to B and E is next to A.
Answer:Both I and II