If A = `{ x: x + 5 = 5}` , then n(A) = _________.

Options

A. 0
B. 1
C. 5
D. 2

Answer

To solve the problem, we need to find the set \( A \) defined by the condition \( x + 5 = 5 \) and then determine the number of elements in that set, denoted as \( n(A) \).

### Step-by-Step Solution:

1. **Understanding the Set Definition**:
The set \( A \) is defined as:
\[ A = \{ x : x + 5 = 5 \} \]
This means we need to find all values of \( x \) that satisfy the equation \( x + 5 = 5 \).

2. **Solving the Equation**:
To find the value of \( x \), we can rearrange the equation:
\[ x + 5 = 5 \]
Subtract 5 from both sides:
\[ x = 5 - 5 \]
Simplifying this gives:
\[ x = 0 \]

3. **Identifying the Elements of Set \( A \)**:
Since we found that \( x = 0 \) is the only solution to the equation, we can express the set \( A \) as:
\[ A = \{ 0 \} \]

4. **Counting the Number of Elements**:
The set \( A \) contains only one element, which is 0. Therefore, the number of elements in set \( A \) is:
\[ n(A) = 1 \]

### Final Answer:
Thus, the answer is:
\[ n(A) = 1 \]