Find the preimage under a constant +4 shift: LKJ : pon :: ? : hgf
Correct Answer: DCB
Introduction / Context:This coding-decoding item uses a constant forward shift across letters. We are given the output and must infer the input by reversing the shift. Such inverse reasoning is routine in alphabet mapping questions.
Given Data / Assumptions:
- LKJ maps to pon with a +4 shift (L→p, K→o, J→n).
- We need a word that maps to hgf via the same +4 rule.
- Case is not semantically important; letter identities are.
Concept / Approach:If output = input shifted by +4, then input = output shifted by −4. Compute each letter accordingly using alphabet positions with wrap-around as needed.
Step-by-Step Solution:
Determine the inverse: h (8) − 4 = d (4), g (7) − 4 = c (3), f (6) − 4 = b (2).Therefore, the input word is d c b → “DCB” in uppercase.Quick check: d+4=h, c+4=g, b+4=f, confirming correctness.Verification / Alternative check:Reapply the forward rule on DCB to see if you recover hgf. The mapping is exact and uniform, so the verification succeeds immediately.
Why Other Options Are Wrong:
- dcle/DBC/dcd: Each contains at least one letter that fails the strict −4 back-shift from h, g, f.
Common Pitfalls:Miscounting by one step or swapping direction (+4 vs −4). Always compute carefully and maintain consistency across all positions.
Final Answer:DCB