⊭ Not True Symbol: Meaning, Uses, and How to Type It

The ⊭ (Not True) symbol is a mathematical logic operator used to indicate that a specific statement does not logically follow from a given set of premises. Officially named "Not True" in the Unicode Standard, this character is a negated version of the double turnstile (⊨). It is frequently used in formal logic, computer science, and set theory to show that a model or structure does not satisfy a specific mathematical formula.

Introduced to digital text standards in Unicode 1.1, the ⊭ symbol resides at code point U+22AD within the Mathematical Operators block. Visually, it features a vertical line intersecting two horizontal lines, completely overlaid with a diagonal slash—the universal mathematical marker for negation. Logicians developed turnstile symbols in the early 20th century to formalize the relationships between logical statements, allowing complex proofs to be written with concise shorthand.

In mathematics and computer science, ⊭ specifically denotes semantic non-consequence. If an equation reads "A ⊭ B", it means that even if statement A is true, statement B isn't necessarily true based on A alone. You will spot this symbol in academic papers covering model theory, semantics, and automated theorem proving. While ⊭ is highly specialized and rarely used in everyday social media messaging, computer science students and math enthusiasts occasionally drop it in forum debates to playfully say "that doesn't prove anything" or "your logic is flawed."

Typing the ⊭ symbol requires a few shortcuts depending on your platform. On Windows, you can use the hexadecimal Alt code by typing 22AD followed by Alt + X in supported applications like Microsoft Word. Mac users can open the Character Viewer (Cmd + Ctrl + Space) and search for "Not True" to drop it into any text field. For programmers and academics writing in LaTeX, the standard command to render this symbol is \nvDash.

The ⊭ symbol belongs to a broader family of turnstile operators. Its direct opposite is the standard double turnstile (⊨), which confirms that a model entails a specific statement. It also shares DNA with the single turnstile (⊢), which deals with syntactic proof rather than semantic truth, and its negated form (⊬), meaning "does not prove."