Six PLK secret agents are arrested and interrogated for several days. An agent tells the truth when all his statements are true, otherwise he lies. A report is drawn up containing the following conclusions:
- If agent $3$ tells the truth and agent $4$ lies then the agent $5$ tells the truth.
- If agent $2$ tells the truth then the same is true for agent $1$ or agent $3$.
- Agent $1$ and $2$ tell the truth when agent $3$ lies or agent $4$ tells the truth.
- If the agent $5$ tells the truth, the agent $6$ does the same.
- Agent $1$ or agent $2$ lie (edit).
- If agent $4$ lies and the agents $5$ and $6$ tell the truth, then the agent $1$ lies or the agent $3$ tells the truth.
- The agent $1$ tell the truth only if the agent $3$ or the agent $6$ lie.
a) Translate the conclusions with simple propositions $a_1, a_2, ..., a_6$ where $a_i$ is defined as 'the agent $i$ tell the truth' and logic connectors .
b) According to the report, who is telling the truth and who lies?
c) Should the interrogation be extended to at least one officer to determine whether his statements are all true or at least one of them is false? Explain.
Could anyone be able to give me a complete answer to this question?
EDIT: I have added the statement number 5.