- Problem 1 (6 marks). Translate each of the following natural language sentences into propositions of the propositional logic language using appropriately the following propositional variables (and no others): mo, ki, al. For each variable, state explicitly the statement it stands for. 1. If you killed the werewolf, then the werewolf is not alive. 2. You killed the werewolf and/or the werewolf is not alive. 3. For the werewolf to be dead, it is necessary that you killed him and you had a motive to kill him. 4. You killed the werewolf, unless you had no motive and/or the werewolf is alive. - Problem 2 (6 marks). The network administrator of a bank called in the cops because a computer program had diverted funds to some unknown account. The system log clearly defined the time period during which the transaction happened. The police has established the following facts: 1. There are exactly three suspects: Alfred, Bert, Christine. Each of the suspects had access to the system during the relevant period, and the log showed that no other user had access. 2. If Alfred is guilty then he has exactly one accomplice. 3. If Bert is guilty, then Christine is guilty and/or Alfred is innocent. 4. If exactly two are guilty then Alfred is one of them. 5. If Bert is innocent, so is Christine. Use exactly three (propositional) variables to translate the above statements into a set A of five propositions. State clearly the meaning of your variables. Then solve this problem (determine who is guilty) by finding a model for A. Show your work using a truth table