Example. Lubs in the domain $\mathbb {B}_\bot \times \mathbb {B}_\bot$ [dt-001B]

$(\bot , \mathit {F}) \sqcup (\mathit {T},\bot ) = (\mathit {T},\mathit {F})$
$(\bot , \mathit {F}) \sqcup (\bot ,\bot ) = (\bot ,\mathit {F})$
$(\bot , \mathit {F}) \sqcup (\mathit {T}, \mathit {T})$ does not exist.