The Mathematical Symbol "True (⊨)"

The ⊨ Symbol in Logic: True or Models

The ⊨ symbol, commonly read as "models" or "entails", is a foundational notation in mathematical logic and model theory. It signifies a specific kind of truth or validity, providing the bridge between syntax (formal languages) and semantics (interpretations or models). In this article, we'll shed light on its meaning and offer illustrative examples.


In logic, the ⊨ sign is employed to convey that a particular statement is true within a given model or that a set of premises logically entails a conclusion. Essentially, it's a way to assert that a specific interpretation or model validates a given formula or statement.


  • Example 1: Logical Entailment:
    If a set of premises \( P \) logically leads to a conclusion \( C \), this relationship can be articulated as \( P ⊨ C \). This indicates that if the premises in \( P \) are true, then \( C \) must also be true.
  • Example 2: Model Validation:
    Consider a structure or model \( M \) and a statement \( S \). If \( S \) is true within the interpretation given by \( M \), then one would write \( M ⊨ S \), expressing that the model \( M \) validates or satisfies the statement \( S \).

To summarize, the ⊨ symbol encapsulates the intricate relationship between formal expressions and their truth values within specific models or interpretations. It's an emblematic notation within logic, underscoring the interplay between abstract formulations and their real-world or conceptual validations.

Mathematical symbol 'True'

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Codes for the ⊨ Symbol

The Symbol
Alt CodeAlt 8872
HTML Code⊨
HTML Entity⊨
CSS Code\22A8
Hex Code⊨

How To Insert the ⊨ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⊨ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8872. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8872;</b>My symbol: ⊨

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &vDash;</b>My symbol: ⊨

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\22A8";}
<span>My symbol:</span>
My symbol: ⊨

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x22A8;</b>My symbol: ⊨
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22A8 to place the ⊨ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⊨ is U+22A8. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 22A8 turns into ⊨. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22A8. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22A8"
document.write("My symbol: " + str)
My symbol: ⊨