π Module 01 Β· Definition
Cardinality of Sets
DEFINITION
Cardinality n(A)
The cardinality of a set is the number of distinct elements contained in that set. It is denoted by n(A) or |A|.
π Example: If A = {a, b, c, d, e}, then n(A) = 5.
If B = {2, 4, 6, 8, 10, 12}, then n(B) = 6.
If B = {2, 4, 6, 8, 10, 12}, then n(B) = 6.
π
Cardinality Formulas
1
n(A βͺ B) = n(A) + n(B) β n(A β© B)
Union of two sets β add both, subtract the overlap
2
n(A β© B) = n(A) + n(B) β n(A βͺ B)
Intersection of two sets β rearranged union formula
3
n(Aβ²) = n(π) β n(A)
Complement of A β elements in universal set but not in A
4
n(A only) = n(A) β n(A β© B)
Elements exclusively in A, not shared with B
5
n(neither) = n(π) β n(A βͺ B)
Elements outside both sets in the universal set
π Module 02 Β· Worked Examples
StepβbyβStep Examples
βοΈ Module 03 Β· Practice
Practice Questions