President Trump will provide written answers under oath in the defamation lawsuit brought by former “Apprentice” contestant Summer Zervos, who claims Trump sexually assaulted her in 2007, a new court filing stated. Lawyers for Trump and Zervos agreed this week to exchange “written answers and objections” to formal written questions by Sept. 28, according to a document filed Friday with the New York State Supreme Court. Rules in New York state require interrogatories to be sworn or verified, according to a source familiar with the system, meaning that false answers could open Trump to charges of perjury.