Complement of Bottom

Theorem

Boolean Algebra

Let $\struct {S, \vee, \wedge, \neg}$ be a Boolean algebra.

Then:

$\neg \bot = \top$

Bounded Lattice

Let $\struct {S, \vee, \wedge, \preceq}$ be a bounded lattice.

Then the bottom $\bot$ has a unique complement, namely $\top$, top.

Also see

• Complement of Top