Question:
Total number of elements in the power set of a set \( A \) containing 15 elements is:
Total number of elements in the power set of a set \( A \) containing 15 elements is:
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The number of elements in the power set of a set with \( n \) elements is \( 2^n \).
Updated On: Apr 23, 2025
- \( 2^{15} \)
- \( 15^2 \)
- \( 2^{15} - 1 \)
- \( 2^{15} - 1 \)
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The Correct Option is A
Solution and Explanation
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 \( 2^{15} \).
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