AMC 8 1986 Problem 22

Alan, Beth, Carlos, and Diana were discussing their possible grades in mathematics class this grading period. Alan said, "If I get an A, then Beth will get an A." Beth said, "If I get an A, then Carlos will get an A." Carlos said, "If I get an A, then Diana will get an A." All of these statements were true, but only two of the students received an A. Which two received A's? $\text{(A)}\ \text{Alan, Beth} \text{(B)}\ \text{Beth, Carlos} \text{(C)}\ \text{Carlos, Diana}$ $\text{(D)}\ \text{Alan, Diana} \text{(E)}\ \text{Beth, Diana}$