Ms. carroll promised that anyone who got all the multiple choice questions right on the upcoming exam would receive an a on the exam. which on of these statements necessarily follows logically?

$\textbf{(a)}\ \text{ if lewis did not receive an a, then he got all of the multiple choice questions wrong.} \\ \qquad\textbf{(b)}\ \text{ if lewis did not receive an a, then he got at least one of the multiple choice questions wrong.} \\ \qquad\textbf{(c)}\ \text{ if lewis got at least one of the multiple choice questions wrong, then he did not receive an a.} \\ \qquad\textbf{(d)}\ \text{ if lewis received an a, then he got all of the multiple choice questions right.} \\ \qquad\textbf{(e)}\ \text{ if lewis received an a, then he got at least one of the multiple choice questions right.}$