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

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

A

`{4,5,6,7}`

B

`{3,4,5,6}`

C

`{4,5,6}`

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
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: \[ A = \{ 3, 4, 5, 6 \} \]
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