If `A={" x:x is an even prime " x in N}` and `B = {"x :x is an odd natural number " x lt 10}`then n ` (A cap B)`= ______

Answer

To solve the problem, we need to find the intersection of two sets, A and B, and then determine the number of elements in that intersection.

**Step 1: Define Set A**
Set A is defined as the set of even prime numbers that belong to the natural numbers (N).
- The only even prime number is 2.
- Therefore, we can write:
\[ A = \{2\} \]

**Step 2: Define Set B**
Set B is defined as the set of odd natural numbers that are less than 10.
- The odd natural numbers less than 10 are: 1, 3, 5, 7, and 9.
- Therefore, we can write:
\[ B = \{1, 3, 5, 7, 9\} \]

**Step 3: Find the Intersection of Sets A and B**
The intersection of two sets, denoted as \(A \cap B\), consists of elements that are common to both sets.
- From Set A, we have the element 2.
- From Set B, we have the elements 1, 3, 5, 7, and 9.
- Since 2 is not present in Set B, there are no common elements between Set A and Set B.
- Therefore, we can write:
\[ A \cap B = \{\} \]

**Step 4: Determine the Number of Elements in the Intersection**
The number of elements in the intersection \(A \cap B\) is the count of elements in the set we found in Step 3.
- Since \(A \cap B\) is an empty set, the number of elements is 0.
- Therefore, we conclude:
\[ n(A \cap B) = 0 \]

**Final Answer:**
\[ n(A \cap B) = 0 \]

---