# Definition:Relative Pseudocomplement

## Definition

Let $(L, \wedge, \vee, \preceq)$ be a lattice.

Let $x, y \in L$.

Then the relative pseudocomplement of $x$ with respect to $y$ is the greatest element $z \in L$ such that $x \wedge z \preceq y$, if such an element exists.

The relative pseudocomplement of $x$ with respect to $y$ is denoted $x \to y$.