 The MC states a sufficient condition but not a necessary condition for conditional probabilistic independence. As such, the MC by itself can never entail that two variables are conditionally or unconditionally dependent. The Minimality and Faithfulness Conditions are two conditions that give necessary conditions for probabilistic independence. (This is employing the terminology of Spirtes et al. (SGS 2000). Pearl (2009) contains a “Minimality Condition” that is slightly different from the one described here.)