Read the situation below and select the best answer for each of the questions that follow. In the Bangla Academy ground there are exactly seven Police supervisors for the security of the Ekushey Book Fair - Mokter, Faruk, Sanwar, Bashir, Anis, Kalam, and Jahangir. These supervisors communicate with each other in two ways: through a wired circuit and by two-way radio. 1. Messages can be sent in only one direction along the wired circuit from Mokter to Faruk, from Faruk to Bashir, from Bashir to Kalam, from Kalam to Jahangir, and from Jahangir to Mokter. II. Messages can be sent in either direction by two-way radio between Faruk and Sanwar, Between Sanwar and Jahangir, and between Bashir and Anis. No other routes of communication are available for sending messages among the seven supervisors. Messages that cannot be sent directly to the intended supervisor are sent through one or more intermediaries, who pass the messages along a possible route. Any supervisor, but only one supervisor, can be an intermediary. In which of the following pairs, a message can be sent using exactly one intermediary?
Explanation: Wired: M\(\to\)F\(\to\)B\(\to\)K\(\to\)J\(\to\)M. Radio (two-way): F\(\leftrightarrow\)S, S\(\leftrightarrow\)J, B\(\leftrightarrow\)A. Exactly one intermediary means a path of 2 steps (Start \(\to\) Int \(\to\) End). A: M to K. M\(\to\)F\(\to\)B\(\to\)K (2 Int). B: S to M. S\(\leftrightarrow\)J\(\to\)M (1 Int: J). S\(\leftrightarrow\)F\(\to\)B\(\to\)K\(\to\)J\(\to\)M (5 Int). The path S \(\to\) J \(\to\) M has one intermediary (J). C: B to F. B\(\to\)K\(\to\)J\(\to\)M\(\to\)F (3 Int). B\(\leftrightarrow\)A (0 Int). B\(\to\)K (0 Int). D: A to S. A\(\leftrightarrow\)B\(\to\)K\(\to\)J\(\leftrightarrow\)S (3 Int). E: J to A. J\(\to\)M\(\to\)F\(\to\)B\(\leftrightarrow\)A (3 Int). J\(\leftrightarrow\)S\(\leftrightarrow\)F\(\to\)B\(\leftrightarrow\)A (3 Int). The pair requiring exactly one intermediary is S to M (via J).
