Heights — Among A, B, C, D, E, F (all different heights), who is the shortest? Statements: I. C is shorter than only B. II. A is taller than only D and F.

Introduction / Context:We must uniquely identify the shortest person using partial ranking facts.

Given Data / Assumptions:

• Six distinct heights: A, B, C, D, E, F.
• I: Only B is taller than C ⇒ B is tallest, C second tallest.
• II: A is taller than only D and F ⇒ D and F are both shorter than A; E is unconstrained.

Concept / Approach:Combine partial orders and see if the minimum (shortest) is forced.

Step-by-Step Solution:

Verification / Alternative check:Construct examples: Case 1 shortest=F (F<D<A<E<C<B). Case 2 shortest=E (E<F<D<A<C<B). Both satisfy I and II.

Why Other Options Are Wrong:

• I alone / II alone: each leaves multiple candidates for shortest.
• Either alone sufficient / Both together sufficient: contradicted by counterexamples.

Common Pitfalls:Assuming E's position without data; assuming D and F order from II (not given).

Final Answer:Both Statements I and II together are not sufficient.