Code-operator logic – under the mapping x→+, <→−, +→÷, >→×, −→=, ÷→>, =→<, determine which statement is true.

Difficulty: Medium

Correct Answer: 5 > 2 + 2 = 10 < 4 x 8

Explanation:


Introduction / Context:
This is a symbol-decoding problem where each comparison or arithmetic operator represents a different real operator. We must decode each expression fully and then evaluate using standard precedence rules, keeping comparisons in their correct roles after mapping.



Given Data / Assumptions:

  • Mapping: x→+, <→−, +→÷, >→×, −→=, ÷→>, =→<.
  • Exactly one of the four options becomes a true statement under this mapping.


Concept / Approach:
Translate symbols before computing. After translation, handle × and ÷ first, then + and −, and finally evaluate comparisons. Chain comparisons should be read in order; once decoded, you typically compare left block to right block with the mapped comparator.



Step-by-Step Solution:

Option C decoding: "5 > 2 + 2 = 10 < 4 x 8"Apply mapping: >→×, +→÷, =→<, <→−, x→+.Thus it becomes: 5 × 2 ÷ 2 < 10 − 4 + 8.Compute left: 5 × 2 ÷ 2 = 5. Compute right: 10 − 4 + 8 = 14. Compare with "<": 5 < 14 is true.


Verification / Alternative check:
Briefly check the others after mapping: they resolve to false inequalities (e.g., yielding 14 = 0 or 1 > 3, which are false).



Why Other Options Are Wrong:

A, B, and D, when decoded, produce incorrect comparisons such as 14=0, 1>3, or 1>8.


Common Pitfalls:
Partially decoding or forgetting to enforce correct operator precedence after translation.



Final Answer:
5 > 2 + 2 = 10 < 4 x 8

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