Which of thefollowing is true?

Options

A. `4 = 7 (mod 5)`
B. `118 = 18 (mod 5)`
C. `110 = 93 (mod 12)`
D. `63=9 (mod 11)`

Answer

To determine which of the given options is true, we need to evaluate each option based on the condition that \( a \equiv b \mod m \) means \( a - b \) is divisible by \( m \).

### Step-by-step Solution:

1. **Evaluate Option 1: \( 4 \equiv 7 \mod 5 \)**
- Calculate \( 4 - 7 = -3 \).
- Check if \(-3\) is divisible by \(5\).
- Since \(-3\) is not divisible by \(5\), Option 1 is **incorrect**.

2. **Evaluate Option 2: \( 118 \equiv 18 \mod 5 \)**
- Calculate \( 118 - 18 = 100 \).
- Check if \(100\) is divisible by \(5\).
- Since \(100\) is divisible by \(5\), Option 2 is **correct**.

3. **Evaluate Option 3: \( 110 \equiv 93 \mod 12 \)**
- Calculate \( 110 - 93 = 17 \).
- Check if \(17\) is divisible by \(12\).
- Since \(17\) is not divisible by \(12\), Option 3 is **incorrect**.

4. **Evaluate Option 4: \( 63 \equiv 9 \mod 11 \)**
- Calculate \( 63 - 9 = 54 \).
- Check if \(54\) is divisible by \(11\).
- Since \(54\) is not divisible by \(11\), Option 4 is **incorrect**.

### Conclusion:
The only true statement is from **Option 2: \( 118 \equiv 18 \mod 5 \)**.