If `X = {x: x is even , x in N and x le 12}` and `Y = {"x is a prime ," x in N and x le 12}` , then `n(X cup Y)` is ______ .

Answer

To solve the problem, we need to find the sets \(X\) and \(Y\) based on the given definitions and then determine the number of elements in the union of these two sets, denoted as \(n(X \cup Y)\).

### Step 1: Define Set \(X\)
Set \(X\) is defined as:
\[ X = \{x : x \text{ is even}, x \in \mathbb{N}, x \leq 12\} \]
The even natural numbers less than or equal to 12 are:
- 2
- 4
- 6
- 8
- 10
- 12

Thus, we can write:
\[ X = \{2, 4, 6, 8, 10, 12\} \]

### Step 2: Define Set \(Y\)
Set \(Y\) is defined as:
\[ Y = \{x : x \text{ is prime}, x \in \mathbb{N}, x \leq 12\} \]
The prime numbers less than or equal to 12 are:
- 2
- 3
- 5
- 7
- 11

Thus, we can write:
\[ Y = \{2, 3, 5, 7, 11\} \]

### Step 3: Find the Union of Sets \(X\) and \(Y\)
The union of two sets \(X\) and \(Y\) is defined as the set of elements that are in either \(X\), \(Y\), or both. We combine the elements of both sets, ensuring that we do not count any duplicates.

Combining the elements:
- From \(X\): 2, 4, 6, 8, 10, 12
- From \(Y\): 2, 3, 5, 7, 11

Now, we list all unique elements:
\[ X \cup Y = \{2, 3, 4, 5, 6, 7, 8, 10, 11, 12\} \]

### Step 4: Count the Number of Elements in the Union
Now we count the number of unique elements in the union \(X \cup Y\):
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 10
- 11
- 12

There are a total of 10 unique elements.

Thus, we conclude that:
\[ n(X \cup Y) = 10 \]

### Final Answer
The number of elements in the union of sets \(X\) and \(Y\) is:
\[ \boxed{10} \]