Step 1: Understanding the Concept:
This is an encoding problem using the same rule as the previous questions. We must apply the rule to the letters of the word 'FRAME'.
Step 2: Key Formula or Approach:
The encoding rules are based on the original letter's position 'm':
- If 'm' is odd, the new position is \(m-1\).
- If 'm' is even, the new position is \(m+1\).
Step 3: Detailed Explanation:
The word to be coded is FRAME. Let's find the position of each letter:
- F is the 6th letter (even).
- R is the 18th letter (even).
- A is the 1st letter (odd).
- M is the 13th letter (odd).
- E is the 5th letter (odd).
Now, apply the encoding rules to each letter:
- F (6, even): The new position is \(6+1 = 7\). The 7th letter is G.
- R (18, even): The new position is \(18+1 = 19\). The 19th letter is S.
- A (1, odd): The new position is \(1-1 = 0\). In cyclic coding, the 0th position is usually Z (26th letter). Let's assume this.
- M (13, odd): The new position is \(13-1 = 12\). The 12th letter is L.
- E (5, odd): The new position is \(5-1 = 4\). The 4th letter is D.
Combining the coded letters, we get G-S-Z-L-D. The code word is GSZLD.
Step 4: Final Answer:
The code word for FRAME is GSZLD, which corresponds to option (C).