Sets Operations
The number of proper subsets of a set containing n elements is
Select the correct option:
Solution
2n−1
- Total Subsets: For a set with n elements, the total number of subsets (including the empty set and the set itself) is 2n.
- Definition of Proper Subset: A set A is a proper subset of B if A⊆B and A=B.
- Constraint: We must exclude exactly one subset: the set itself.
- Formula: Total Subsets - 1 = 2n−1.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- sets operations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
2n−1
- Total Subsets: For a set with n elements, the total number of subsets (including the empty set and the set itself) is 2n.
- Definition of Proper Subset: A set A is a proper subset of B if A⊆B and A=B.
- Constraint: We must exclude exactly one subset: the set itself.
- Formula: Total Subsets - 1 = 2n−1.
This easy difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of sets operations. It appeared in the 2025 exam.
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