Question

The number of subsets of a set consisting of 10 elements is?

• A. \( 10! \)
• B. 11
• C. 12
• D. \( 2^{10} \)

Hint:

The number of subsets of a set with \( n \) elements is always \( 2^n \).

Answer 1

The Correct Option is D

For any set with \( n \) elements, the total number of subsets (including the empty set and the set itself) is \( 2^n \). This is because for each element, we have two choices: either include it in the subset or exclude it.
Thus, for a set with 10 elements, the number of subsets is: \[ 2^{10} = 1024 \] So, the correct answer is \( 2^{10} \).