Vacuous truth is the truth of a conditional whose hypothesis is false. In
particular, a universally quantified assertion
over an empty set is vacuously true.
For any predicate 
, the assertion 
is true
because there is no element for which 
is false (Morris and Morris 2025,
pp. 83-84).
An empty conjunction likewise has value true, the identity element for AND. This is the logical counterpart of an empty product having value 1. By comparison, an empty disjunction has value false, corresponding to an empty sum equal to 0.
