📐 Module 01 · 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|.
📌 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.
📐
Cardinality Formulas
1
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Union of two sets — add both, subtract the overlap
2
n(A ∩ B) = n(A) + n(B) − n(A ∪ B)
Intersection of two sets — rearranged union formula
3
n(A′) = n(𝕌) − n(A)
Complement of A — elements in universal set but not in A
4
n(A only) = n(A) − n(A ∩ B)
Elements exclusively in A, not shared with B
5
n(neither) = n(𝕌) − n(A ∪ B)
Elements outside both sets in the universal set
📝 Module 02 · Worked Examples
Step‑by‑Step Examples
✏️ Module 03 · Practice
Practice Questions
📝 Written Solution
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