Conjunctions/disjunctions with many conjuncts/disjuncts
According to the associative laws, (p?q)?r ? p?(q?r). So it does
not matter where we put parentheses, and we can just write p?q?r.
Same thing for more than 3 conjuncts --- no need in parentheses.
The proposition p1 ? p2 ? … ? pn is unambiguous: it is true if
and only if all of its conjuncts are true.
Similarly for disjunction. The truth value of p1 ? p2 ? ... ? pn is
well defined: it is T if and only if (at least) one of the disjuncts is
Generalized De Morgan’s laws:
- ?(p1 ? p2 ? … ? pn) ? ?p1 ? ?p2 ? ... ? ?pn
- ?(p1 ? p2 ? … ? pn) ? ?p1 ? ?p2 ? ... ? ?pn