Study the statements and conclusions below. Each symbol used in the statements…

Concept: In statement-and-conclusion inequality puzzles, each coded symbol first has to be translated into a standard relation (>, <, ≥, ≤, =, ≠). Once every statement is decoded, any statements sharing a common term can be chained (transitivity) to derive a definite relation between the two end terms. A conclusion is valid only if it necessarily follows from the derived relations — one that contradicts a derived relation, or one that is not always guaranteed, is invalid.

Application:

1. Decode the statements: A % B means A is greater than B; C = E means C is not less than E, i.e. C is greater than or equal to E; D * B means D is not greater than B, i.e. D is less than or equal to B.

2. Combine A > B and D ≤ B. Since D ≤ B and B < A, it follows that D < A, i.e. A is definitely greater than D.

3. Check conclusion i (A # D, i.e. A is less than D): this directly contradicts the derived relation A > D, so conclusion i does not hold.

4. Check conclusion ii (C * E, i.e. C is less than or equal to E): the statement only gives C ≥ E. This is compatible with C = E (making the conclusion true) but also with C > E (making it false), so conclusion ii is not guaranteed to be true in every case.

Cross-check:

Assign values consistent with every statement, e.g. B = 2, A = 5 (A > B), D = 1 (D ≤ B), E = 3, C = 4 (C ≥ E). Conclusion i asks whether A < D, i.e. 5 < 1, which is false. Conclusion ii asks whether C ≤ E, i.e. 4 ≤ 3, which is also false. Both conclusions fail under this valid assignment, confirming neither is guaranteed by the statements.

Result: Since conclusion i is directly contradicted and conclusion ii is not always guaranteed, neither conclusion follows definitely from the statements.