Question

Total number of elements in the power set of a set \( A \) containing 15 elements is:

• A. \( 2^{15} \)
• B. \( 15^2 \)
• C. \( 2^{15} - 1 \)
• D. \( 2^{15} - 1 \)

Hint:

The number of elements in the power set of a set with \( n \) elements is \( 2^n \).

Answer 1

The Correct Option is A

The power set of a set with \( n \) elements contains \( 2^n \) elements. This is because each element of the set can either be included or excluded from a subset. Given that the set \( A \) contains 15 elements, the number of subsets (or elements in the power set) is: \[ 2^{15} \] Thus, the correct answer is \( 2^{15} \).