Set Theory
Essential formulas and concepts in set theory
Union-Intersection (Inclusion-Exclusion for two sets)
\(|A \cup B| = |A| + |B| - |A \cap B|\)
Variables:
- \(A and B are sets; |X| denotes the number of elements in set X.\)
Description/Usage:
Calculates the size of the union of two sets by adding their sizes and subtracting the overlap (which was counted twice). This principle generalizes to more sets with alternating plus and minus of intersections (inclusion-exclusion principle).
Mathematical concept visualization
Size of Power Set
\(| \mathcal{P}(A) | = 2^{|A|}\)
Variables:
Description/Usage:
The number of possible subsets of a set \(A\) is \(2^{|A|}\) (each element either in or out of a subset). For instance, a set with 3 elements has \(2^3=8\) subsets.
Mathematical concept visualization