Seven persons A, B, C, D, E, F and G travel by three cars X, Y, Z. A and another two of them travel by X. Only E travels with G. C travels by Z, but B does not travel by Y. Besides, A and B do not travel by the same car. Then which of the following are correct? I. No one travels alone. II. Only D travels with F. III. Only C travels with B. Select the answer using the code given below.

• Car X contains A and two others, totaling 3 persons; since A and B are in different cars, B is not in X.

• Car Z contains C; since B does not travel by Y, B must travel by Z, so Z contains at least C and B.

• Only E travels with G, meaning E and G form a pair in the same car; they cannot be in X (which has 3 people including A) or Z (which has C and B, and adding E/G would make 4, but let's check capacity constraints or remaining slots).

• Let's deduce the cars: X has A + 2 others. Z has C + B. The remaining persons are D, E, F, G. E and G must be together. If E and G are in Y, then Y has E and G. The remaining persons for X are D and F (since B is in Z, C is in Z, E/G in Y). So X = {A, D, F}, Y = {E, G}, Z = {B, C}.

• Check statement I: No one travels alone. X has 3, Y has 2, Z has 2. This is correct.

• Check statement II: Only D travels with F. In X, A also travels with D and F. So D travels with A and F. This statement is incorrect.

• Check statement III: Only C travels with B. In Z, only C and B are present. This is correct.

• Therefore, statements I and III are correct, which corresponds to option (b).