Editing Propositional formula (section)

=== Commutative and associative laws ===

Both AND and OR obey the [[commutative law]] and [[associative law]]:
* Commutative law for OR: ( a &or; b ) ≡ ( b &or; a )
* Commutative law for AND: ( a & b ) ≡ ( b & a )
* Associative law for OR: (( a &or; b ) &or; c ) ≡ ( a &or; (b &or; c) )
* Associative law for AND: (( a & b ) & c ) ≡ ( a & (b & c) )

'''Omitting parentheses in strings of AND and OR''': The connectives are considered to be unary (one-variable, e.g. NOT) and binary (i.e. two-variable AND, OR, IMPLIES). For example:
: ( (c & d) &or; (p & c) &or; (p & ~d) ) above should be written ( ((c & d) &or; (p & c)) &or; (p & ~(d) ) ) or possibly ( (c & d) &or; ( (p & c) &or; (p & ~(d)) ) )
However, a truth-table demonstration shows that the form without the extra parentheses is perfectly adequate.

'''Omitting parentheses with regards to a single-variable NOT''': While ~(a) where a is a single variable is perfectly clear, ~a is adequate and is the usual way this [[literal (mathematical logic)|literal]] would appear. When the NOT is over a formula with more than one symbol, then the parentheses are mandatory, e.g. ~(a &or; b).