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Recursive definition
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===Well formed formula=== The notion of a [[well-formed formula]] (wff) in propositional logic is defined recursively as the smallest set satisfying the three rules: # {{math|p}} is a wff if {{math|p}} is a propositional variable. # {{math|Β¬ p}} is a wff if {{math|p}} is a wff. # {{math|(p β’ q)}} is a wff if {{math|p}} and {{math|q}} are wffs and β’ is one of the logical connectives β¨, β§, β, or β. The definition can be used to determine whether any particular string of symbols is a wff: * {{math|(''p'' β§ ''q'')}} is a wff, because the propositional variables {{math|''p''}} and {{math|''q''}} are wffs and {{math|β§}} is a logical connective. * {{math|Β¬ (''p'' β§ ''q'')}} is a wff, because {{math|(''p'' β§ ''q'')}} is a wff. * {{math|(Β¬ ''p'' β§ Β¬ ''q'')}} is a wff, because {{math|Β¬ ''p''}} and {{math|Β¬ ''q''}} are wffs and {{math|β§}} is a logical connective.
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