The number of subsets of a set containing n elements is
(a) \(n\)
(b) \(2^n-1\)
(c) \(n^2\)
(d) \(2^n\)
Solution
If a set contains \(n\) elements, then each element has two choices:
- either included in a subset
- or not included in a subset
Therefore, total number of subsets
\[ =2 \times 2 \times 2 \cdots \text{(n times)} \]
\[ =2^n \]
Answer
\[ \boxed{2^n} \]
Correct option: (d)