From your example, perhaps you mean "competence does not imply knowledge" or more accurately in fact "lack of competence implies lack of knowledge" i.e. !competence -> !knowledge, in that competence && !knowledge is common but !competence && knowledge is rare.
From your example, perhaps you mean "competence does not imply knowledge" or more accurately in fact "lack of competence implies lack of knowledge" i.e. !competence -> !knowledge, in that competence && !knowledge is common but !competence && knowledge is rare.