Symbol re-mapping puzzle: If “>” denotes addition (+), “<” denotes subtraction (−), “+” denotes division (÷), “^” denotes multiplication (×), “−” denotes equality (=), “x” denotes greater-than (>) and “=” denotes less-than (<), choose the statement that is mathematically correct after applying these replacements.

Introduction / Context:
This is an operator-replacement reasoning problem. Each symbol must be replaced consistently, then the resulting arithmetic statement is checked for truth. Such questions test attention to detail, operator precedence, and careful translation.

Given Data / Assumptions:

• Mappings: “>” → +, “<” → −, “+” → ÷, “^” → ×, “−” → =, “x” → >, “=” → <.
• Evaluate with normal arithmetic precedence (×, ÷ before +, −) and then compare.

Concept / Approach:
Translate each option using the mapping, simplify the left side, and check whether the comparison (or equality) is true.

Step-by-Step Solution:
(A) 13 > 7 < 6 + 2 = ^ 4 → 13 + 7 − 6 ÷ 2 < × 4 (ill-formed because “=<×4” yields a comparison against a missing left factor). (B) 9 > 5 > 4 − 18 + 9 > 16 → 9 + 5 + 4 = 18 ÷ 9 + 16. Compute LHS: 9 + 5 + 4 = 18. RHS: 18 ÷ 9 + 16 = 2 + 16 = 18. Statement is true. (C) 9 < 3 < 2 > 1 x 8 ^ 2 → 9 − 3 − 2 + 1 > 8 × 2 → 5 > 16 (false). (D) 28 + 4 ^ 2 = 6 ^ 4 + 2 → 28 ÷ 4 × 2 < 6 × 4 ÷ 2 → 14 < 12 (false).

Verification / Alternative check:
Re-evaluate (B) carefully with precedence to confirm both sides equal 18. Others either become false or malformed.

Why Other Options Are Wrong:

• (A) Translation results in an invalid structure (comparison against an incomplete product).
• (C) Resolves to 5 > 16 (false).
• (D) Resolves to 14 < 12 (false).

Common Pitfalls:
Mixing symbol roles, ignoring that “−” denotes equality, and losing operator precedence while simplifying.

Final Answer:
9 > 5 > 4 - 18 + 9 > 16