∪ Union Symbol
The union sign (∪) combines two sets — A ∪ B is everything in A, in B, or in both. It is the counterpart of intersection ∩.
Also known as: union sign, union symbol, set union symbol latex, union sign math, cup symbol.
Codes
| Symbol | ∪ | |
| Intersection | ∩ · U+2229 | |
| N-ary union | ⋃ · U+22C3 | |
| Unicode | U+222A | |
| HTML entity (named) | ∪ | |
| HTML entity (decimal) | ∪ | |
| HTML entity (hex) | ∪ | |
| CSS | \222A | |
| LaTeX | \cup | |
| Windows Alt code | Alt + 8746 |
How to type ∪ (Union Symbol)
Alt + 8746 works in apps that accept decimal-Unicode Alt input. In Word type 222A then Alt + X; elsewhere press Win + . (period) and search “union”. (Intersection ∩ has the short code Alt + 239.)
No default keystroke. Open Character Viewer (Control + Cmd + Space) and search “union”, or copy ∪ above.
Type 222A, then press Alt + X to convert it to ∪.
Insert → Special characters, then search “union” — or inside an Equation type \cup.
Use \cup for the binary operator and \bigcup for the large form with limits, as in \bigcup_{i=1}^{n} A_i. Intersection is \cap and \bigcap.
Usage
- A ∪ B is the set of elements in A, in B, or in both: {1, 2} ∪ {2, 3} = {1, 2, 3}. Elements are not counted twice.
- ∪ is “or”, ∩ is “and” — that is the fastest way to keep them apart. In probability, P(A ∪ B) = P(A) + P(B) − P(A ∩ B); the subtraction is there precisely because the overlap would otherwise be counted twice.
- Which cup to use: ∪ (U+222A) is the binary operator between two sets. ⋃ (U+22C3) is the large n-ary version that takes limits above and below, the way ∑ does. They are different characters and the large one looks wrong inline.
- Do not substitute the letter U or ∨ (U+2228, logical or). ∪ joins sets; ∨ joins propositions; U is a letter. All three appear in the same textbooks, which is exactly why the wrong one gets pasted.