Encoded operators and inequalities — choose the true relation: Mapping: A → '+', M → '×', D → '÷', G → '>', L → '<'. Which option is logically correct when decoded and evaluated with standard precedence?

Introduction / Context: We decode each string using the provided mapping for arithmetic and comparison operators, then evaluate both sides with standard precedence to see which inequality is true.

Given Data / Assumptions:

• A = +, M = ×, D = ÷, G = >, L = <
• Use ×/÷ before +/− with left-to-right tie-breaking.

Concept / Approach: Translate and compute each side numerically, then check the indicated comparison ( > or < ). Only one option should produce a true statement.

Step-by-Step Checks (concise): (a) 4 + 5 ÷ 3 > 6 + 2 × 3 → 5.67 > 12 → false (b) 4 + 5 × 4 < 6 ÷ 2 + 8 → 24 < 11 → false (c) 4 ÷ 2 + 4 > 6 ÷ 2 + 4 → 6 > 7 → false (d) 4 + 3 × 2 < 4 ÷ 2 × 6 → 10 < 12 → true

Why Other Options Are Wrong: Each computes to a false inequality once decoded and properly evaluated. Typical errors when solving include ignoring precedence or misreading the mapping for M and D.

Common Pitfalls: Doing addition before finishing ×/÷, or evaluating comparisons before both sides are fully simplified.

Final Answer: 4A 3M 2L 4D 2M 6