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COMEDK2021MathematicsSets and Relations

Total number of elements in the power set of A containing 15 elements is

Options

  1. A2¹⁵
  2. B15²
  3. C2¹⁵⁻¹
  4. D2¹⁵-1

Correct answer

A. 2¹⁵

Step-by-step solution

The power set of a set A , denoted by P(A) , is the set of all subsets of A . If a set A contains n elements, then the number of elements in its power set P(A) is given by 2^ n . Given that the set A contains 15 elements, we have n = 15 . Therefore, the total number of elements in the power set of A is 2¹⁵ . Answer: 2¹⁵

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