Symbol encoding check — select the correct statement: Encoding: δ → '+', • → '−', γ → '×', η → '÷', ω → '=', β → '>', α → '<'. Which option becomes a true relation after decoding and evaluating with standard precedence?
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A3 γ 6 η 2 δ 8 • 4 ω 5
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B3 η 6 γ 2 δ 8 • 4 β 5
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C3 γ 6 • 2 δ 8 η 4 α 5
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D3 δ 6 • 2 γ 8 η 4 ω 5
Answer
Correct Answer: 3 δ 6 • 2 γ 8 η 4 ω 5
Explanation
Introduction / Context: The problem encodes arithmetic and comparison symbols. After decoding, we evaluate both sides of each candidate with standard precedence and check whether the stated relation is true.
Given Data / Assumptions:
- δ=+, •=−, γ=×, η=÷, ω==, β=>, α=<
- Precedence: ×, ÷ before +, −; left-to-right within the same tier.
Concept / Approach: Systematically decode each option and compute numerical values on both sides of the relation (either =, >, or <). Exactly one option should hold true.
Step-by-Step Check (true option): (d) 3 δ 6 • 2 γ 8 η 4 ω 5 → 3 + 6 − 2 × 8 ÷ 4 = 5 Compute ×/÷: 2 × 8 = 16; 16 ÷ 4 = 4 Now +/−: 3 + 6 − 4 = 5 — equality holds
Why Other Options Are Wrong (sketch): (a) 3×6÷2+8−4 = 13 ≠ 5; (b) 3÷6×2+8−4 = 5 so 5 > 5 is false; (c) 3×6−2+8÷4 = 18, and 18 < 5 is false.
Common Pitfalls: Misreading ω as > or <, or evaluating +/− before finishing ×/÷ in long strings of operations.
Final Answer: 3 δ 6 • 2 γ 8 η 4 ω 5