Logic symbols to copy and paste
The 64 most common symbols of logic, boolean algebra and set theory in one grid. Select one to copy it, as the character itself or as LaTeX, HTML or a Unicode code point, and see how to type it in Word.
Matches names, LaTeX commands, HTML entities and code points. In the grid, arrow keys move between symbols and Enter copies one.
Symbol grid
Connectives (18 symbols)
Not, and, or, exclusive or, the conditional and biconditional, NAND, NOR and the two constants.
Quantifiers (4 symbols)
For predicate logic: statements about every x, or some x.
Proof and metalogic (8 symbols)
Symbols that talk about statements and arguments rather than joining them.
Boolean algebra (4 symbols)
The engineering notation for AND, OR and NOT used with logic gates.
Sets (23 symbols)
Membership, subsets, the set operations and the number sets.
Relations (9 symbols)
Equality, equivalence and order.
How to type logic symbols
Copying from a page works anywhere, but each place you write has a way of its own that is quicker once you know it.
Microsoft Word
Type the hex code from the panel and press Alt+X: 2227 becomes ∧. Word reads hex digits back from the cursor, so after a letter A to F or a digit, select the code first. Insert › Equation also takes LaTeX-style commands such as \wedge.
LaTeX
Use the command in math mode, between $ signs. 15 of the commands, such as \therefore, come from the amssymb package, which the panel flags; add \usepackage{amssymb} to the preamble.
HTML
A page saved as UTF-8 can hold the symbol itself. Otherwise use the named entity, such as ∧, or the numeric one, ∧, which works for every character. A < in text is safest written <, since a < followed by a letter starts a tag.
Windows and macOS
On Windows 11, Win+. opens the emoji panel, whose symbols tab has many of these. On a Mac, Ctrl+Cmd+Space opens the Character Viewer, which can search by name.
Whole formulas in LaTeX and HTML
The same formulas written three ways, each converted symbol by symbol from the table on this page. Note the space after a command such as \lnot before a letter: without it LaTeX reads \lnotp as one unknown command.
¬(p ∧ q) ≡ ¬p ∨ ¬q
- LaTeX
- \lnot(p \land q) \equiv \lnot p \lor \lnot q
- HTML
- ¬(p ∧ q) ≡ ¬p ∨ ¬q
∀x ∃y (x < y)
- LaTeX
- \forall x \exists y (x < y)
- HTML
- ∀x ∃y (x < y)
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
- LaTeX
- A \cap (B \cup C) = (A \cap B) \cup (A \cap C)
- HTML
- A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
A̅ · B̅ = (A + B)′
- LaTeX
- \overline{A} \cdot \overline{B} = (A + B)'
- HTML
- A̅ · B̅ = (A + B)′
To check what a formula means, paste it into the propositional logic calculator for its truth table, or a boolean expression into the boolean algebra calculator.
Look-alikes and common mistakes
Several of these symbols have twins that fonts draw almost the same way. They are different characters, so a search for one will not find the other.
- U+2228, U+0076 The or sign is not the letter v. A search, a screen reader or a parser reads them differently.
- U+00AC, U+2212, U+002D The not sign, the minus sign and the hyphen are three characters. Only ¬ means not.
- U+2205, U+00D8, U+03C6 The empty set is not the Scandinavian letter Ø or the Greek phi, though fonts draw them alike.
- U+0394, U+2206 Greek capital delta and the increment sign look identical; symmetric difference is usually typed with Δ.
- U+2032, U+0027 The prime is a separate character from the apostrophe. Both are used for NOT A; the prime looks better in print.
- U+00B7, U+22C5 The middle dot and the dot operator both mean AND in boolean algebra. LaTeX \cdot prints the dot operator.
- U+007E, U+223C The keyboard tilde and the tilde operator. LaTeX \sim gives the tilde operator.
Meanings shift between books too. ⊂ is a proper subset in some and any subset in others, which is why ⊆ and ⊊ exist; ≡ can mean logically equivalent or the biconditional; ⊃ is the conditional in older logic books and superset in set theory. The propositional logic and set notation pages explain each in context.
Printable logic symbols table
All 64 symbols in one table with their codes, ready to print. Symbols with two jobs, such as ⊃ and ≡, appear once.
| Symbol | Name | Unicode | HTML | LaTeX |
|---|---|---|---|---|
| Connectives | ||||
| ¬Negation | Negation | U+00AC | ¬ | \lnot |
| ~Tilde | Tilde | U+007E | ~ | \sim |
| ∧Conjunction | Conjunction | U+2227 | ∧ | \land |
| ∨Disjunction | Disjunction | U+2228 | ∨ | \lor |
| ⊕Exclusive or | Exclusive or | U+2295 | ⊕ | \oplus |
| ⊻XOR (veebar) | XOR (veebar) | U+22BB | ⊻ | \veebar * |
| →Conditional | Conditional | U+2192 | → | \to |
| ⇒Implies | Implies | U+21D2 | ⇒ | \Rightarrow |
| ⊃Horseshoe | Horseshoe | U+2283 | ⊃ | \supset |
| ↔Biconditional | Biconditional | U+2194 | ↔ | \leftrightarrow |
| ⇔If and only if | If and only if | U+21D4 | ⇔ | \Leftrightarrow |
| ≡Logically equivalent | Logically equivalent | U+2261 | ≡ | \equiv |
| ↑Sheffer stroke | Sheffer stroke | U+2191 | ↑ | \uparrow |
| ⊼NAND | NAND | U+22BC | ⊼ | \barwedge * |
| ↓Peirce arrow | Peirce arrow | U+2193 | ↓ | \downarrow |
| ⊽NOR | NOR | U+22BD | ⊽ | — |
| ⊤Top | Top | U+22A4 | ⊤ | \top |
| ⊥Bottom | Bottom | U+22A5 | ⊥ | \bot |
| Quantifiers | ||||
| ∀For all | For all | U+2200 | ∀ | \forall |
| ∃There exists | There exists | U+2203 | ∃ | \exists |
| ∄There does not exist | There does not exist | U+2204 | ∄ | \nexists * |
| ∃!There exists exactly one | There exists exactly one | U+2203 U+0021 | ∃! | \exists! |
| Proof and metalogic | ||||
| ⊢Turnstile | Turnstile | U+22A2 | ⊢ | \vdash |
| ⊨Double turnstile | Double turnstile | U+22A8 | ⊨ | \models |
| ∴Therefore | Therefore | U+2234 | ∴ | \therefore * |
| ∵Because | Because | U+2235 | ∵ | \because * |
| ∎End of proof | End of proof | U+220E | ∎ | \blacksquare * |
| □Box | Box | U+25A1 | □ | \Box * |
| ◇Diamond | Diamond | U+25C7 | ◇ | \Diamond * |
| ⊣Left tack | Left tack | U+22A3 | ⊣ | \dashv |
| Boolean algebra | ||||
| ·Middle dot | Middle dot | U+00B7 | · | \cdot |
| +Plus | Plus | U+002B | + | + |
| ′Prime | Prime | U+2032 | ′ | ' |
| A̅Overline | Overline | U+0305 | ̅ | \overline{A} |
| Sets | ||||
| ∈Element of | Element of | U+2208 | ∈ | \in |
| ∉Not an element of | Not an element of | U+2209 | ∉ | \notin |
| ∋Contains as member | Contains as member | U+220B | ∋ | \ni |
| ⊂Subset | Subset | U+2282 | ⊂ | \subset |
| ⊆Subset or equal | Subset or equal | U+2286 | ⊆ | \subseteq |
| ⊊Proper subset | Proper subset | U+228A | ⊊ | \subsetneq * |
| ⊇Superset or equal | Superset or equal | U+2287 | ⊇ | \supseteq |
| ∪Union | Union | U+222A | ∪ | \cup |
| ∩Intersection | Intersection | U+2229 | ∩ | \cap |
| ∖Set difference | Set difference | U+2216 | ∖ | \setminus |
| ∅Empty set | Empty set | U+2205 | ∅ | \emptyset |
| ℘Weierstrass p | Weierstrass p | U+2118 | ℘ | \wp |
| 𝒫Power set | Power set | U+1D4AB | 𝒫 | \mathcal{P} |
| ×Cartesian product | Cartesian product | U+00D7 | × | \times |
| ∁Complement | Complement | U+2201 | ∁ | \complement * |
| ΔSymmetric difference | Symmetric difference | U+0394 | Δ | \Delta |
| ⊖Circled minus | Circled minus | U+2296 | ⊖ | \ominus |
| ℕNatural numbers | Natural numbers | U+2115 | ℕ | \mathbb{N} * |
| ℤIntegers | Integers | U+2124 | ℤ | \mathbb{Z} * |
| ℚRational numbers | Rational numbers | U+211A | ℚ | \mathbb{Q} * |
| ℝReal numbers | Real numbers | U+211D | ℝ | \mathbb{R} * |
| ℂComplex numbers | Complex numbers | U+2102 | ℂ | \mathbb{C} * |
| Relations | ||||
| =Equals | Equals | U+003D | = | = |
| ≠Not equal to | Not equal to | U+2260 | ≠ | \neq |
| ≢Not equivalent | Not equivalent | U+2262 | ≢ | \not\equiv |
| ≈Approximately equal to | Approximately equal to | U+2248 | ≈ | \approx |
| <Less than | Less than | U+003C | < | < |
| ≤Less than or equal to | Less than or equal to | U+2264 | ≤ | \leq |
| >Greater than | Greater than | U+003E | > | > |
| ≥Greater than or equal to | Greater than or equal to | U+2265 | ≥ | \geq |
* needs \usepackage{amssymb}. — means no command in base LaTeX or amssymb.
Questions
How do I copy and paste a logic symbol?
Select its tile and it is copied straight away: the "Copy as" buttons choose whether you get the symbol itself, its LaTeX command, its HTML code or its Unicode code point. For ∧ those are ∧, \land, ∧ and U+2227. The symbol panel, beside the grid or under it on a phone, has copy buttons for the symbol, its code point, its HTML codes (named, hex and decimal) and its LaTeX command.
How do I type logic symbols in Word?
Type the symbol's hex code and press Alt+X straight after it: 2227 then Alt+X gives ∧. Word reads hex digits backwards from the cursor, so if the code follows a letter A to F or a digit, select just the code before pressing Alt+X. Alt+X on a symbol you have already typed turns it back into its code.
Which logic symbols need amssymb in LaTeX?
15 of the 64 symbols here: \veebar, \barwedge, \nexists, \therefore, \because, \blacksquare, \Box, \Diamond, \subsetneq, \complement, \mathbb{N}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}, \mathbb{C}. Add \usepackage{amssymb} to the preamble. The everyday connectives, \lnot, \land, \lor, \to and \leftrightarrow, are in base LaTeX.
What is the difference between → and ⇒?
Most books write the conditional, a connective inside a formula, as p → q. Many use ⇒ for implication as a claim about formulas, that p → q holds in every case, or between the lines of a proof. Some books use ⇒ for the conditional itself, and older ones use ⊃, so follow the convention of whatever you are reading.
What is the difference between ⊢ and ⊨?
Γ ⊢ φ (turnstile) says φ can be derived from Γ using the rules of a proof system: it is about proofs. Γ ⊨ φ (double turnstile) says every assignment that makes Γ true also makes φ true: it is about truth. Soundness and completeness theorems are the statements that the two agree.
How do I write NOT A with a bar over it?
Type A and then the combining overline, U+0305, which draws a bar over the character before it: A̅. In LaTeX write \overline{A}, which also stretches over a longer expression. In plain text a prime, A′, or an apostrophe, A', means the same and is easier to type.