Question:
The number of subsets of a set containing $n$ elements is:
The number of subsets of a set containing $n$ elements is:
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This includes the empty set and the set itself.
Updated On: Apr 8, 2026
- $n^{2}$
- $2^{n}$
- $2n$
- $n$
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The Correct Option is B
Solution and Explanation
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)
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)
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