Question

The number of subsets of a set containing $n$ elements is:

• A. $n^{2}$
• B. $2^{n}$
• C. $2n$
• D. $n$

Hint:

This includes the empty set and the set itself.

Answer 1

The Correct Option is B

Step 1: Concept
Each element in a set has two choices: either to be in a subset or not to be in it.
Step 2: Analysis
For $n$ elements, the total number of combinations is $2 \times 2 \times \dots \times 2$ ($n$ times).
Step 3: Conclusion
Total number of subsets $= 2^{n}$.
Final Answer: (B)