This cheat sheet lists 18 Logic symbols from nyuyo. It includes because, double-turnstile, end-of-proof and more. Each entry shows the symbol, its meaning, LaTeX command, Unicode code point and HTML entity. Every entry also shows how to read an example aloud.
because
Character
∵
Name
Because
Meaning
Placed before a reason that supports the next step of an argument. In LaTeX it needs the amssymb package. Compare with Therefore and Implies.
LaTeX
\because
Unicode
U+2235
HTML entity
∵
Example expression
∵ x > 0
Read aloud
because x is greater than zero
Related symbols
Therefore, Implies, If and Only If
double-turnstile
Character
⊨
Name
Double Turnstile
Meaning
States that the formula on the right is true in every model where the assumptions on the left are true. With a single structure on the left, it says the formula holds in that structure.
LaTeX
\models
Unicode
U+22A8
HTML entity
⊨
Example expression
Γ ⊨ φ
Read aloud
gamma entails phi
Related symbols
Turnstile, Implies
end-of-proof
Character
∎
Name
End of Proof
Meaning
Marks the end of a proof, taking the place of the older QED. It is also called the tombstone or Halmos symbol, and a hollow square □ is used the same way.
LaTeX
\blacksquare
Unicode
U+220E
HTML entity
∎
Example expression
… so n is even. ∎
Read aloud
so n is even, end of proof
Related symbols
Therefore, Because, Square
exclusive-or
Character
⊻
Name
Exclusive Or
Meaning
Joins two statements into one that is true when exactly one of them is true. In LaTeX it needs the amssymb package.
LaTeX
\veebar
Unicode
U+22BB
HTML entity
⊻
Example expression
P ⊻ Q
Read aloud
P exclusive or Q
Related symbols
Logical Or, Logical And, Logical Not, Direct Sum
for-all
Character
∀
Name
For All
Meaning
The universal quantifier. It states that what follows holds for every object in the given range.
LaTeX
\forall
Unicode
U+2200
HTML entity
∀
Example expression
∀x ∈ ℝ, x² ≥ 0
Read aloud
for all x in the real numbers, x squared is greater than or equal to zero
Related symbols
There Exists, There Does Not Exist, Element Of
if-and-only-if
Character
⇔
Name
If and Only If
Meaning
States that two statements imply each other, so they are either both true or both false.
LaTeX
\Leftrightarrow
Unicode
U+21D4
HTML entity
⇔
Example expression
P ⇔ Q
Read aloud
P if and only if Q
Related symbols
Implies, Left Right Arrow
implied-by
Character
⇐
Name
Implied By
Meaning
States that the statement on the right implies the statement on the left. It often marks the converse direction of an if-and-only-if proof.
LaTeX
\Leftarrow
Unicode
U+21D0
HTML entity
⇐
Example expression
x² = 4 ⇐ x = 2
Read aloud
x squared equals four is implied by x equals two
Related symbols
Implies, If and Only If
implies
Character
⇒
Name
Implies
Meaning
States that if the statement on the left is true, then the statement on the right is also true.
LaTeX
\Rightarrow
Unicode
U+21D2
HTML entity
⇒
Example expression
x = 2 ⇒ x² = 4
Read aloud
x equals two implies x squared equals four
Related symbols
If and Only If, Therefore, Right Arrow, Logical And
and
Character
∧
Name
Logical And
Meaning
Joins two statements into one that is true only when both statements are true.
LaTeX
\land
Unicode
U+2227
HTML entity
∧
Example expression
P ∧ Q
Read aloud
P and Q
Related symbols
Logical Or, Logical Not
not
Character
¬
Name
Logical Not
Meaning
Reverses the truth value of a statement: true becomes false and false becomes true.
LaTeX
\neg
Unicode
U+00AC
HTML entity
¬
Example expression
¬P
Read aloud
not P
Related symbols
Logical And, Logical Or
or
Character
∨
Name
Logical Or
Meaning
Joins two statements into one that is true when at least one of them is true.
LaTeX
\lor
Unicode
U+2228
HTML entity
∨
Example expression
P ∨ Q
Read aloud
P or Q
Related symbols
Logical And, Logical Not, Union, Implies
nand
Character
⊼
Name
Nand
Meaning
Joins two statements into one that is false only when both of them are true. It is the negation of and. In LaTeX it needs the amssymb package.
LaTeX
\barwedge
Unicode
U+22BC
HTML entity
⊼
Example expression
P ⊼ Q ⇔ ¬(P ∧ Q)
Read aloud
P nand Q if and only if not both P and Q
Related symbols
Logical And, Logical Not
there-does-not-exist
Character
∄
Name
There Does Not Exist
Meaning
States that no object in the given range makes what follows true. In LaTeX it needs the amssymb package.
LaTeX
\nexists
Unicode
U+2204
HTML entity
∄
Example expression
∄x ∈ ℝ, x² = −1
Read aloud
there is no real number x such that x squared equals minus one
Related symbols
There Exists, For All, Logical Not
there-exists
Character
∃
Name
There Exists
Meaning
The existential quantifier. It states that at least one object in the given range makes what follows true.
LaTeX
\exists
Unicode
U+2203
HTML entity
∃
Example expression
∃x ∈ ℤ, x + 3 = 0
Read aloud
there exists an integer x such that x plus three equals zero
Related symbols
For All, There Does Not Exist
exists-unique
Character
∃!
Name
There Exists Unique
Meaning
The uniqueness quantifier. It states that exactly one object in the given range makes what follows true.
LaTeX
\exists!
Unicode
U+2203 U+0021
HTML entity
∃!
Example expression
∃!x ∈ ℝ, x + 3 = 0
Read aloud
there exists a unique real number x such that x plus three equals zero
Related symbols
There Exists, For All, There Does Not Exist
therefore
Character
∴
Name
Therefore
Meaning
Placed before a conclusion that follows from the preceding lines. In LaTeX it needs the amssymb package.
LaTeX
\therefore
Unicode
U+2234
HTML entity
∴
Example expression
∴ x = 5
Read aloud
therefore x equals five
Related symbols
Because, Implies
top
Character
⊤
Name
Top
Meaning
Stands for a statement that is always true. In order theory it also names the greatest element of a lattice.
LaTeX
\top
Unicode
U+22A4
HTML entity
⊤
Example expression
P ∨ ¬P ≡ ⊤
Read aloud
P or not P is equivalent to top
Related symbols
Perpendicular, Logical Or
turnstile
Character
⊢
Name
Turnstile
Meaning
States that the formula on the right can be proved from the assumptions on the left using the rules of a formal system.
LaTeX
\vdash
Unicode
U+22A2
HTML entity
⊢
Example expression
Γ ⊢ φ
Read aloud
gamma proves phi
Related symbols
Double Turnstile, Implies, Therefore, Top
FAQ
How many Logic symbols are on this page?
This page lists 18 Logic symbols, including because, double-turnstile, end-of-proof.
How do I type Logic symbols in LaTeX?
Each symbol on this page has its LaTeX command shown next to it, for example \barwedge, \because, \blacksquare. Copy the command into your maths mode.
What are the Unicode code points for Logic symbols?
Every symbol lists its Unicode code point, such as U+00AC, U+21D0, U+21D2, so you can insert it in documents and web pages.
How do I write Logic symbols in HTML?
Each entry shows its HTML entity where one exists, for example ∧, ∵, ∃. You can paste it directly into your page.
How do I read Logic symbols aloud?
Each symbol has an example expression and a spoken version, such as … so n is even. ∎, ∀x ∈ ℝ, x² ≥ 0, ∃!x ∈ ℝ, x + 3 = 0 read as because x is greater than zero, for all x in the real numbers, x squared is greater than or equal to zero, gamma entails phi.