State whether the Roman number CXVVI is valid or not? Give reasons for your answer.

Options

A. valid
B. not valid
C. cannot be determined
D. none of the above

Answer

To determine whether the Roman numeral CXVVI is valid or not, we can follow these steps:

### Step 1: Break down the Roman numeral
The Roman numeral CXVVI can be broken down into its components:
- C = 100
- X = 10
- V = 5
- V = 5
- I = 1

### Step 2: Analyze the components
Now, let's analyze the components:
- The numeral C (100) is followed by X (10), which is valid.
- The numeral X (10) is followed by V (5), which is also valid.
- However, after V (5), we have another V (5) and then an I (1).

### Step 3: Check for valid combinations
In Roman numerals, the same letter can be repeated up to three times. The numeral V can only appear once in a valid sequence. Therefore, having two V's in succession (VV) is not allowed.

### Step 4: Conclusion
Since the sequence VV is not valid in Roman numerals, we conclude that the Roman numeral CXVVI is not valid.

### Final Answer
The Roman numeral CXVVI is not valid because it contains two consecutive V's, which is not allowed in Roman numeral representation.

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