∩
∩ Intersection Symbol
The intersection symbol (∩) gives the elements two sets have in common: A ∩ B is everything in both A and B.
Also known as: intersection sign, intersection symbol, set intersection, and symbol set theory.
Codes
| Symbol | ∩ | |
| Union (opposite) | ∪ · U+222A | |
| Unicode | U+2229 | |
| HTML entity (named) | ∩ | |
| HTML entity (decimal) | ∩ | |
| HTML entity (hex) | ∩ | |
| CSS | \2229 | |
| LaTeX | \cap | |
| Windows Alt code | Alt + 239 |
How to type ∩ (Intersection Symbol)
WindowsAlt + 239
Hold Alt and type 239 on the numeric keypad, then release Alt (or type 2229 then Alt + X in Word).
Mac
No default keystroke. Open Character Viewer (Control + Cmd + Space) and search “intersection”, or copy ∩ above.
Microsoft Word2229, Alt + X
Type 2229, then press Alt + X to convert it to ∩.
Google Docs
Insert → Special characters, then search “intersection”. In an equation, \cap followed by a space also works.
LaTeX\cap
Use \cap in math mode: A \cap B. \bigcap gives the large operator for indexed intersections.
Usage
- A ∩ B is the intersection of A and B — the set of elements in both. If A = {1,2,3} and B = {2,3,4}, then A ∩ B = {2,3}.
- ∩ and ∪ are the pair to learn together: ∩ (U+2229) is intersection (“and”), ∪ (U+222A) is union (“or”, everything in either set). The cup opens upward; the cap opens downward.
- In probability, P(A ∩ B) is the chance that both A and B happen.
- Which one to use: ∩ (U+2229) is the ordinary binary operator between two sets. ⋂ (U+22C2, n-ary intersection) is the big version used with an index underneath, the way ∑ relates to +. Do not substitute a lowercase n — it is a different character and will not read as an operator.