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Mathematics · JEE I SETS

हिन्दी

Given below are two statements: Statement I: The empty set \( \phi \) is an infinite set because it contains no elements to count. Statement II: Two finite sets are equal if and only if they have the same number of elements. In the light of the above statements, choose the most appropriate answer from the options given below:

  1. A
    Both Statement I and Statement II are correct.
  2. B
    Both Statement I and Statement II are incorrect.
  3. C
    Statement I is correct but Statement II is incorrect.
  4. D
    Statement I is incorrect but Statement II is correct.
View Answer & Solution

Correct answer · Option B

Both Statement I and Statement II are incorrect.

Explanation

By definition, the empty set is finite (with \( n(\phi) = 0 \)), so Statement I is false. Two sets are equal only if they have exactly the same elements, not merely the same count, so Statement II is false.
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