MAJESTIC Word Transformation: Vowel Count Analysis
This solution explains the process of transforming the word MAJESTIC based on specific rules for consonants and vowels and determines the final count of vowels in the transformed sequence.
Understanding the MAJESTIC Transformation Rules
The core task is to modify each letter in the word MAJESTIC. The rules depend on whether a letter is a vowel or a consonant:
- Consonant Rule: Each consonant is replaced by the letter immediately preceding it in the English alphabet.
- Vowel Rule: Each vowel (A, E, I, O, U) is replaced by the letter immediately succeeding it in the English alphabet.
To clarify the transformation, we can think about the position of each letter in the alphabet (where A is the 1st letter, B is the 2nd, and so on). Let \(P(X)\) denote the position of letter \(X\).
- The transformation for a consonant \(C\) results in a new letter \(C'\) where \(P(C') = P(C) - 1\).
- The transformation for a vowel \(V\) results in a new letter \(V'\) where \(P(V') = P(V) + 1\).
Applying the Rules to MAJESTIC
First, let's identify the letters in the word MAJESTIC and classify them:
Word: MAJESTIC
Letters: M, A, J, E, S, T, I, C
Classification:
- Vowels: A, E, I
- Consonants: M, J, S, T, C
Step-by-Step Letter Transformation
We will now apply the defined rules to each letter of MAJESTIC:
| Original Letter | Type | Transformation Rule Applied | New Letter |
|---|---|---|---|
| M | Consonant | Previous letter (\(P(M)=13 \rightarrow P(M')=12\)) | L |
| A | Vowel | Next letter (\(P(A)=1 \rightarrow P(A')=2\)) | B |
| J | Consonant | Previous letter (\(P(J)=10 \rightarrow P(J')=9\)) | I |
| E | Vowel | Next letter (\(P(E)=5 \rightarrow P(E')=6\)) | F |
| S | Consonant | Previous letter (\(P(S)=19 \rightarrow P(S')=18\)) | R |
| T | Consonant | Previous letter (\(P(T)=20 \rightarrow P(T')=19\)) | S |
| I | Vowel | Next letter (\(P(I)=9 \rightarrow P(I')=10\)) | J |
| C | Consonant | Previous letter (\(P(C)=3 \rightarrow P(C')=2\)) | B |
Constructing the New Word
Combining the transformed letters gives us the new group of letters.
The original word MAJESTIC transforms into: LBIFRSJB.
Identifying Vowels in the Resulting Sequence
The final step is to count how many vowels (A, E, I, O, U) are present in the new sequence LBIFRSJB.
Let's check each letter:
- L is a consonant.
- B is a consonant.
- I is a vowel.
- F is a consonant.
- R is a consonant.
- S is a consonant.
- J is a consonant.
- B is a consonant.
By examining the letters, we find there is only one vowel ('I') in the sequence LBIFRSJB.
Final Count of Vowels
Therefore, the number of vowels present in the new group of letters formed after the transformation is one.
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