Cancellation of Meet in Boolean Algebra

Theorem

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

Let $a, b, c \in S$.

Let:

\(\ds a \wedge c\)

\(=\)

\(\ds b \wedge c\)

\(\ds a \wedge \neg c\)

\(=\)

\(\ds b \wedge \neg c\)

Then:

$a = b$

Proof

Follows from Cancellation of Join in Boolean Algebra through the Duality Principle

$\blacksquare$

Also see

• Cancellation of Join in Boolean Algebra