Let `A={x:x` is a positive multiple of `2` less than `20` , `x in N}` then `n(A)` is

Options

A. 7
B. 8
C. 6
D. 9

Answer

To solve the problem, we need to determine the set \( A \) defined as follows:

\[ A = \{ x : x \text{ is a positive multiple of } 2 \text{ less than } 20, x \in \mathbb{N} \} \]

### Step 1: Identify the positive multiples of 2
The positive multiples of 2 are obtained by multiplying 2 by natural numbers. The first few positive multiples of 2 are:
- \( 2 \times 1 = 2 \)
- \( 2 \times 2 = 4 \)
- \( 2 \times 3 = 6 \)
- \( 2 \times 4 = 8 \)
- \( 2 \times 5 = 10 \)
- \( 2 \times 6 = 12 \)
- \( 2 \times 7 = 14 \)
- \( 2 \times 8 = 16 \)
- \( 2 \times 9 = 18 \)

### Step 2: List the multiples of 2 that are less than 20
Now, we will list the multiples of 2 that are less than 20:
- The multiples are: \( 2, 4, 6, 8, 10, 12, 14, 16, 18 \)

### Step 3: Count the elements in set \( A \)
Now, we will count the elements in set \( A \):
- The elements are: \( 2, 4, 6, 8, 10, 12, 14, 16, 18 \)
- The total number of elements is \( 9 \).

### Conclusion
Thus, the number of elements in set \( A \) is:
\[ n(A) = 9 \]