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The following lists some propositional formula equivalences. Remember that we use the symbol as a relation between two WFFs, not as a connective inside a WFF.In these, , , and are meta-variables standing for any WFF.

Propositional logic equivalences
Double Complementation
Complement
Identity
Dominance
Idempotency
Absorption
Redundancy
DeMorgan's Laws
Associativity
Commutativity
Distributivity

Equivalences for implication are omitted above for brevity and for tradition. They can be derived, using the definition a b a b .

For example, using Identity and Commutativity, we have b b b b b .

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Source:  OpenStax, Fundamentals of computer engineering. OpenStax CNX. Oct 17, 2007 Download for free at http://cnx.org/content/col10347/1.4
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