Question

If \( A = \{ x : x \text{ is an integer and } x^2 - 9 \geq 0 \} \), \[ B = \{ x : x \text{ is a natural number and } 2 \leq x \leq 5 \}, \quad C = \{ x : x \text{ is a prime number} \leq 4 \} \] Then \( (B - C) \cup A \) is:

• A. \( \{2, 3, 4\} \)
• B. \( \{3, 4, 5\} \)
• C. \( \{2, 3, 5\} \)
• D. \( \{-3, 3, 4\} \)

Hint:

To perform set operations like union and difference, make sure to identify the correct elements based on the set conditions.

Answer 1

The Correct Option is D

- The set \( A = \{-3, -2, -1, 1, 2, 3\} \) satisfies \( x^2 - 9 \geq 0 \). - The set \( B = \{2, 3, 4\} \), where \( x \) is a natural number and \( 2 \leq x \leq 5 \). - The set \( C = \{2, 3\} \), where \( x \) is a prime number less than or equal to 4. Now, \( B - C = \{4\} \). Therefore, \[ (B - C) \cup A = \{4\} \cup \{-3, -2, -1, 1, 2, 3\} = \{-3, 3, 4\} \]