Set Theory and Logic Symbols (∈ ∪ ∩ ∅ ∀ ∃) and How to Type Them
Quick answer: set theory uses ∈ (element of), ⊂ ⊆ (subset), ∪ (union), ∩ (intersection), ∖ (difference) and ∅ (empty set); logic adds ∀ ∃ ¬ ∧ ∨. Only ∩ (Alt+239) and ¬ (Alt+0172) have Windows Alt codes. Type the rest in Word with the code in the table above and Alt+X, with equation commands such as \in, or copy them.
Quick reference: every method
Every Alt code below is verified against the real Windows code pages — where none exists we say so, rather than list one that won’t work.
| Char | Name | Windows | Mac | HTML | Word (Alt+X) | Unicode |
|---|---|---|---|---|---|---|
| ∈ | Element Of | Copy / paste | Copy / paste | ∈ |
2208 + Alt+X |
U+2208 |
| ∉ | Not An Element Of | Copy / paste | Copy / paste | ∉ |
2209 + Alt+X |
U+2209 |
| ⊂ | Subset Of | Copy / paste | Copy / paste | ⊂ |
2282 + Alt+X |
U+2282 |
| ⊆ | Subset Of Or Equal To | Copy / paste | Copy / paste | ⊆ |
2286 + Alt+X |
U+2286 |
| ∪ | Union | Copy / paste | Copy / paste | ∪ |
222A + Alt+X |
U+222A |
| ∩ | Intersection | Alt+239 |
Copy / paste | ∩ |
2229 + Alt+X |
U+2229 |
| ∖ | Set Minus | Copy / paste | Copy / paste | ∖ |
2216 + Alt+X |
U+2216 |
| ∅ | Empty Set | Copy / paste | Copy / paste | ∅ |
2205 + Alt+X |
U+2205 |
| ℕ | Double-Struck Capital N | Copy / paste | Copy / paste | ℕ |
2115 + Alt+X |
U+2115 |
| ℤ | Double-Struck Capital Z | Copy / paste | Copy / paste | ℤ |
2124 + Alt+X |
U+2124 |
| ℚ | Double-Struck Capital Q | Copy / paste | Copy / paste | ℚ |
211A + Alt+X |
U+211A |
| ℝ | Double-Struck Capital R | Copy / paste | Copy / paste | ℝ |
211D + Alt+X |
U+211D |
| ∀ | For All | Copy / paste | Copy / paste | ∀ |
2200 + Alt+X |
U+2200 |
| ∃ | There Exists | Copy / paste | Copy / paste | ∃ |
2203 + Alt+X |
U+2203 |
| ¬ | Not Sign | Alt+0172 |
Option+L |
¬ |
00AC + Alt+X |
U+00AC |
| ∧ | Logical And | Copy / paste | Copy / paste | ∧ |
2227 + Alt+X |
U+2227 |
| ∨ | Logical Or | Copy / paste | Copy / paste | ∨ |
2228 + Alt+X |
U+2228 |
Set symbols and their meaning
| Symbol | Meaning | Example | Word equation / LaTeX |
|---|---|---|---|
| ∈ ∉ | is / is not an element of | 3 ∈ A | \in \notin |
| ⊆ ⊂ | subset (or equal) / subset | A ⊆ B | \subseteq \subset |
| ∪ | union | A ∪ B | \cup |
| ∩ | intersection | A ∩ B | \cap |
| ∖ | set difference | A ∖ B | \setminus |
| ∅ | empty set | A ∩ B = ∅ | \emptyset |
| ℕ ℤ ℚ ℝ ℂ | natural, integer, rational, real, complex numbers | x ∈ ℝ | \mathbb{R} (LaTeX) |
Logic symbols
| Symbol | Meaning | Word equation / LaTeX |
|---|---|---|
| ∀ | for all | \forall |
| ∃ | there exists | \exists |
| ¬ | not | \neg |
| ∧ ∨ | and, or | \wedge \vee |
| ⇒ ⇔ | implies, if and only if | \Rightarrow \Leftrightarrow |
| ∴ ∵ | therefore, because | \therefore \because |
How to type them
- Windows Alt codes: only ∩
Alt+239(no zero) and ¬Alt+0172. - Word: code + Alt+X (∈ 2208, ∪ 222A, ∅ 2205, ∀ 2200), or an equation (Alt+=) with the commands above. See symbols in Word.
- Mac: ¬ is Option+L; everything else via the Character Viewer (search "element", "union", "empty set").
- Google Docs: Insert → Special characters, or Insert → Equation.
- LaTeX: the commands above inside
$…$; ℝ and friends need\mathbb{}from the amssymb package. See LaTeX math symbols.
Look-alikes
- ∈ vs ε: the element sign is not the Greek epsilon, even though some fonts make them similar.
- ∅ vs Ø vs ⌀: empty set, Scandinavian letter, diameter sign.
- ∧ vs ^: the keyboard caret ^ is not the logical "and".
- ∖ vs \: the set-minus sign is a maths character; the backslash is a keyboard character with other uses.
Related: calculus symbols, geometry symbols, our intersection symbols collection and the math symbols hub.
Frequently asked questions
How do I type the "element of" symbol ∈?
There is no Alt code. In Word type 2208 and press Alt+X, or type \in in an equation. On a Mac use the Character Viewer and search "element". You can also copy ∈ from this page.
What is the difference between ⊂ and ⊆?
⊆ means "is a subset of or equal to". ⊂ is used by some authors for a proper subset (strictly smaller) and by others for any subset, so say which convention you use.
Is the empty set ∅ the same as the letter Ø?
No. ∅ (U+2205) is the empty set sign. Ø is a Danish and Norwegian letter, and ⌀ is the diameter sign. They look alike but are different characters.
Do any set symbols have Alt codes?
Only two: ∩ is Alt+239 and the logical not sign ¬ is Alt+0172. All the others are above 255, so use Word's Alt+X or copy and paste.
Looking for something else? Browse 1,000+ copy-paste symbols, the full Alt Codes finder, or the emoji picker.