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Mathematics · JEE I SETS

हिन्दी

Let \( A = \{x \in \mathbb{N} : x \le 50 \text{ and } x \text{ is a multiple of } 3\} \) and \( B = \{x \in \mathbb{N} : x \le 50 \text{ and } x \text{ is a multiple of } 5\} \). The number of subsets of \( A \cap B \) is:

  1. A
    \( 8 \)
  2. B
    \( 4 \)
  3. C
    \( 16 \)
  4. D
    \( 32 \)
View Answer & Solution

Correct answer · Option A

\( 8 \)

Explanation

\( A \cap B \) consists of multiples of \( \text{lcm}(3, 5) = 15 \) up to 50, which are \( \{15, 30, 45\} \). There are \( 3 \) elements, so the number of subsets is \( 2^3 = 8 \).
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