Question

If
A=(2) (4, 5) (3) {1, 2, 3) (4) (6, 7) A = {x: x is an even number less than 10} and 
B= {x: x is a prime number less than 10} 
then n(∩) is 

• A. 0
• B. 1
• C. 2
• D. None of these

Answer 1

The Correct Option is B

Step 1: Define the sets \( A \) and \( B \).

\[ A = \{x : x \text{ is an even number less than 10}\}. \]

The even numbers less than 10 are \( 2, 4, 6, 8 \). Thus:

\[ A = \{2, 4, 6, 8\}. \]

\[ B = \{x : x \text{ is a prime number less than 10}\}. \]

The prime numbers less than 10 are \( 2, 3, 5, 7 \). Thus:

\[ B = \{2, 3, 5, 7\}. \]

Step 2: Find the intersection \( A \cap B \).

The intersection \( A \cap B \) contains all elements that are common to both \( A \) and \( B \). Comparing the elements of \( A \) and \( B \):

\[ A = \{2, 4, 6, 8\}, \quad B = \{2, 3, 5, 7\}. \]

The only common element is \( 2 \). Thus:

\[ A \cap B = \{2\}. \]

Step 3: Find \( n(A \cap B) \).

The number of elements in \( A \cap B \) is:

\[ n(A \cap B) = 1. \]

Final Answer: The value of \( n(A \cap B) \) is \( \mathbf{1} \), which corresponds to option \( \mathbf{(2)} \).