Boolean Algebra Again?

There has always been a hint in the air that what we have been doing with propositions mirrors what we did with Boolean algebras. Let's see what evidence we have so far on this connection.

All of these appear in Boolean algebra. To be sure that we have a Boolean algebra all we have to do is to make sure that the axioms of Boolean algebra hold for propositions (page 16). Let's look at a few for a start.

Table 9: Towards a proof of commutativity

$p$ $q$ $p+q$ $p+q$
0 0 0 0
0 1 1 1
1 0 1 1
1 1 1 1

From here we can see that $(p + q) \to (q + p) $ and $(q + p) \to(p + q)$. So + (either or) in propositional logic are the same.


  1. Prove that $pq = qp$.
  2. Prove that the remaining axioms are also true.

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