How to Write the Not-Independent Symbol in LaTeX

To typeset “$X$ is not independent of $Y$” in LaTeX, place a negation slash over the full double-perpendicular independence symbol. The centernot package provides a convenient way to center that slash.

Recommended notation

A common notation for independence is $X \perp\!\!\!\perp Y$. Negate the whole relation with \centernot:

X \centernot{\perp\!\!\!\perp} Y

The \centernot command supplies the spacing of a relation, like $=$ or $\leq$.

Complete example

This minimal document uses the centernot package. No additional package is needed for the displayed equation.

\documentclass{article}
\usepackage{centernot}

\begin{document}

\[
X \centernot{\perp\!\!\!\perp} Y
\]

\end{document}

Compile the document with a standard LaTeX engine such as pdfLaTeX. The result shows a slash centered over both perpendicular marks, expressing that $X$ and $Y$ are not independent.

Conditional independence

For variables that are not independent given $Z$, add a conditioning bar and $Z$:

X \centernot{\perp\!\!\!\perp} Y \mid Z

This is read as “$X$ is not independent of $Y$ given $Z$.” The corresponding independence statement is commonly written $X \perp\!\!\!\perp Y \mid Z$.

Why not use \not directly?

A quick alternative is \not\!\perp\!\!\!\perp. It may work in some settings, but \not is designed to negate a following symbol. With a hand-built double-perpendicular symbol, the slash can appear over only the first mark or be positioned awkwardly. \centernot{...} explicitly centers the slash over the entire expression.

The double-perpendicular symbol itself is usually assembled from two \perp commands with negative spaces. The exact number of \! spacing commands is a typographic convention, so a document or journal may use a slightly different construction. The important point is to apply the negation to the complete independence symbol.

Common mistakes

• Forgetting the package: \centernot is not defined by basic LaTeX. Include \usepackage{centernot} in the preamble.
• Negating only one perpendicular: \not\perp places a slash over a single perpendicular mark, not necessarily over the double symbol.
• Adding an unnecessary wrapper: \centernot supplies relation spacing itself, so an outer \mathrel{...} is redundant.
• Confusing perpendicularity with independence: A lone $\perp$ can mean geometric perpendicularity. The double-perpendicular form is a common convention for probabilistic independence.