To determine which statements are true, let's analyze each option provided:

• Statement A: "Full duplex communication is bidirectional."
  Explanation: Full duplex communication allows data transmission in both directions simultaneously. An example is a telephone conversation where both parties can talk and listen at the same time.
  Conclusion: This statement is true.
• Statement B: "FM radio is an example of simplex communication."
  Explanation: Simplex communication is one-way communication. FM radio is a form of broadcast where the radio station transmits information and the listeners receive it without sending information back.
  Conclusion: This statement is true.
• Statement C: "Walkie-talkie is an example of full duplex communication."
  Explanation: Walkie-talkies operate in half-duplex mode, meaning that communication is bidirectional but not simultaneous. Each party must take turns to speak by pressing a button.
  Conclusion: This statement is false.
• Statement D: "In half duplex communication both devices can send and receive data at the same time."
  Explanation: Half duplex communication allows communication in both directions, but not at the same time. The devices must take turns to transmit or receive data.
  Conclusion: This statement is false.
• Statement E: "A landline telephone is an example of half duplex communication."
  Explanation: A landline telephone is an example of full duplex communication, where both parties can converse simultaneously.
  Conclusion: This statement is false.

Based on the analysis above, the correct answer is A and B Only, as both statements A and B are true.