Subset Calculator - Multi-Tools

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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