Complement of Top

Theorem

Boolean Algebra

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

Then:

$\neg \top = \bot$

Bounded Lattice

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

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

Also see

• Complement of Bottom