If `A={x:x in N and 3 le x lt7}`, then `A = ?`

Options

A. `{4,5,6,7}`
B. `{3,4,5,6}`
C. `{4,5,6}`
D. None of these

Answer

To solve the problem, we need to determine the elements of the set \( A \) based on the given conditions.

### Step-by-Step Solution:

1. **Identify the Set Definition**:
The set \( A \) is defined as \( A = \{ x : x \in \mathbb{N} \text{ and } 3 \leq x < 7 \} \). Here, \( \mathbb{N} \) represents the set of natural numbers.

2. **Determine the Range of \( x \)**:
The condition \( 3 \leq x < 7 \) means that \( x \) can take values starting from 3 up to, but not including, 7.

3. **List the Natural Numbers in the Range**:
The natural numbers that satisfy \( 3 \leq x < 7 \) are:
- \( x = 3 \)
- \( x = 4 \)
- \( x = 5 \)
- \( x = 6 \)

4. **Form the Set**:
Therefore, the set \( A \) can be written as:
\[ A = \{ 3, 4, 5, 6 \} \]

### Final Answer:
Thus, the set \( A \) is:
\[ A = \{ 3, 4, 5, 6 \} \]