Which of the following Roman numerals are not valid? Support your answer with reasons.
a. VX b. LC c. VVXI d. CCC

Answer

To determine which of the given Roman numerals are not valid, let's analyze each option step by step:

### Step 1: Analyze Option a - VX
- Roman numeral V represents 5 and X represents 10.
- In Roman numeral rules, a smaller numeral cannot precede a larger numeral unless it is a specific case (like IV for 4).
- Here, V (5) is placed before X (10), which is not allowed.
- **Conclusion**: VX is not a valid Roman numeral.

### Step 2: Analyze Option b - LC
- Roman numeral L represents 50 and C represents 100.
- According to Roman numeral rules, L (50) cannot precede C (100) because L is smaller than C.
- In valid Roman numeral combinations, a smaller numeral can only precede a larger numeral in specific cases (like XL for 40).
- **Conclusion**: LC is not a valid Roman numeral.

### Step 3: Analyze Option c - VVXI
- Roman numeral V represents 5, X represents 10, and I represents 1.
- The numeral VV is problematic because V cannot be repeated. The maximum repetition allowed is three (like III for 3).
- Additionally, V cannot come before X, as it is smaller.
- **Conclusion**: VVXI is not a valid Roman numeral.

### Step 4: Analyze Option d - CCC
- Roman numeral C represents 100.
- CCC means 100 + 100 + 100 = 300.
- According to Roman numeral rules, repeating C three times is valid.
- **Conclusion**: CCC is a valid Roman numeral.

### Final Summary:
- Invalid Roman numerals: a. VX, b. LC, c. VVXI
- Valid Roman numeral: d. CCC