Subset Calculator
Result
Subset Concepts
Key concepts in set theory:
- Subset: A set A is a subset of set B if every element of A is also in B
- Proper Subset: A set A is a proper subset of B if A is a subset of B but A ≠ B
- Power Set: The set of all possible subsets of a given set
- Cardinality: The number of elements in a set
For a set with n elements:
- Number of all subsets = 2ⁿ
- Number of proper subsets = 2ⁿ - 1
- Number of elements in power set = 2ⁿ
Example Problems
Example 1: Set A = {1, 2, 3}
All Subsets:
- ∅ (empty set)
- {1}
- {2}
- {3}
- {1, 2}
- {1, 3}
- {2, 3}
- {1, 2, 3}
Total subsets: 2³ = 8
Proper subsets: 2³ - 1 = 7
Example 2: Set B = {a, b}
All Subsets:
- ∅ (empty set)
- {a}
- {b}
- {a, b}
Total subsets: 2² = 4
Proper subsets: 2² - 1 = 3
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