Yes, when a book uses an example as a definition, it's frustrating. I think that "dual" means exchanging "and" with "or" and 0 with 1, as well as negating every variable. So the dual of is . I also think that the original equation has implicit universal quantifiers:
i.e., it is viewed as a univesal law, as opposed to an equation that one has to solve. When universally quantified,
is equivalent to
Of course, negating variables may not be a part of this particular definition of "dual".