# Definition:Pseudocomplement

## Definition

Let $(L, \wedge, \vee, \preceq)$ be a lattice with smallest element $\bot$.

Let $x, x^* \in L$.

Then $x^*$ is the pseudocomplement of $x$ iff

$x^*$ is the greatest element of $L$ such that $x \wedge x^* = \bot$.