Set Theory Guide
Set Notation Reference
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| โช | Union | Elements in A or B | {1,2}โช{2,3}={1,2,3} |
| โฉ | Intersection | Elements in both A and B | {1,2}โฉ{2,3}={2} |
| โ | Complement | Elements not in A | โแตคA |
| โ | Difference | Elements in A but not B | {1,2,3}โ{2}={1,3} |
| โ | Subset | A is subset of B | {1,2}โ{1,2,3} |
| โ | Proper Subset | AโB and Aโ B | {1,2}โ{1,2,3} |
| โ | Empty Set | Set with no elements | {}=โ |
| โ | Element of | x is in set A | 2โ{1,2,3} |
| โ | Not element of | x is not in set A | 5โ{1,2,3} |
| |A| | Cardinality | Number of elements | |{a,b,c}|=3 |
| ร | Cartesian Product | All ordered pairs (a,b) | AรB |
| ๐ซ(A) | Power Set | All subsets of A | ๐ซ({1,2})={{"{โ ,{1},{2},{1,2}}"}} |
De Morgan's Laws
Law 1
(A โช B)แถ = Aแถ โฉ Bแถ
Complement of union = intersection of complements
Law 2
(A โฉ B)แถ = Aแถ โช Bแถ
Complement of intersection = union of complements
Inclusion-Exclusion Principle
|A โช B| = |A| + |B| - |A โฉ B|
|A โช B โช C| = |A| + |B| + |C| - |AโฉB| - |AโฉC| - |BโฉC| + |AโฉBโฉC|