Mary thought her uncle was involved in activities against the law.

against 是介词，意思是"反对、违反"，表示对立或相反的关系。 the 是定冠词，用于特指某个或某些事物。 law 是名词，意思是"法律、法规"。 against the law 是一个固定短语，意思是"违法的、违反法律的"。