Each of implication, conjunction, and truth is a "right adjoint" in categorial semantics. This means that to each of these operations is associated a category in which the operation is a final object.
Truth is final in the base category.
Conjunction of A and B is final among propositions implying both A and B separately.
Logical implication from C to D is final among propositions Z such that the conjunction of Z and C implies D.
Visually, final objects look like sinks in a category, hence they're "negative."
Positive connctives are left adjoints, hence initial, hence they look like sources in a category.
Generally speaking, the negative component is more expressive than the positive component because conjunction has a right adjoint, logical implication, while disjunction only has a left adjoint if the logic satisfies excluded middle (correct me if I'm wrong, please).