The conjunction of two propositions, p, q is the proposition p & q . It is true if, and only if, each of p, q is true. The medievals were interested in whether there exist different kinds of conjunction subject to a weaker condition, since while a book is a conjunction of the assertions it contains, it seems harsh to say that it is wholly false if one of them is false. See also truth-function.
Philosophy dictionary. Academic. 2011.