Question

If $A = \{x \in \mathbb{N} : x^2 < 25\}$ and $B = \{x \in \mathbb{N} : x \text{ is even}, x \leq 10\}$, then $A \cap B$ is:

• A. {2, 4}
• B. {4}
• C. {2, 4, 6}
• D. {2, 4, 6, 8, 10}

Hint:

List all elements of both sets first for easy comparison.

Answer 1

The Correct Option is A

Step 1: Concept
Set theory - Intersection.

Step 2: Analysis
$A = \{1, 2, 3, 4\}$ (since $x^2 < 25$ and $x$ is a natural number).
$B = \{2, 4, 6, 8, 10\}$.

Step 3: Calculation
$A \cap B = \{x : x \in A \text{ and } x \in B\} = \{2, 4\}$.

Step 4: Conclusion
The intersection is {2, 4}. Final Answer: (A)