The famous adventurer Georgia Jones is now in a never-before-visited hall of the Bent Pyramid of Dahcour erected by King Snefru. The room contains 3 stelae, each placed in front of a separate closed room of a massive stone.

One and only one of the rooms contains

Snefrou's treasure. The stelae each have a easy to read inscription. Georgia's work has clearly shown that 2 stelae have

true inscriptions while only one is false, but the identity of the false stele remains completely unknown to him (Snefru had this unfortunate habit when he

stated 3 things to always state exactly one wrong). Here are the entries

of each of the 3 stelae translated and reported by Georgia Jones herself:

Stela 1: The treasure is either behind this stela or behind stela 2, and the inscription of Stela 3 is false.

Stela 2: If the treasure is not here then the inscription of Stela 1 is false.

Stele 3: If the inscription of Stele 1 is false then the treasure is in the room behind stele 2.

You must help Georgia Jones choose the room that contains the treasure. To achieve this, you are going to give deductive reasoning which will establish the part, among the three, which

contains the treasure. I ask you to produce your deductive reasoning by following the following 3 steps in order:

(a) Define useful propositions and combine them using logical operators to get a list of true propositions that translate

Georgia's knowledge

Jones about Snefrou's treasure as he entered the room with three stelae. He

This is a list of hypotheses for future deductive reasoning that will allow us to locate the treasure.

(b) Give a proposition using those you defined in (a), which represents the expected conclusion of deductive reasoning that determines where the Snefrou's treasure is found. In other words, you are trying to determine the part at treasure and express your choice in propositional logic. For example, if you have a proposition p: "The treasure is in room 2 (the one behind stele 2)" and that

you think it is then the expected conclusion is simply p. Nothing more complicated than ca.

(c) Consider the list of propositions given in (a)

as the hypotheses of a deductive reasoning. Provide valid deductive reasoning from the assumptions that allows Georgia Jones to reach the conclusion you have indicated

at point (b). That conclusion must be where the treasure is. Your deductive reasoning should also clearly state the inference rules and equivalence relations used to arrive at the conclusion.

the picture shows what i have done but the part c) is not done right could you help me please

also in my notes, a : position of the treasure behind the stele 1

b: position of the tresor behind the stele 2

a) Stele 1=p(ab)r stlle 2=q(bp) a= porition du trisets stele 3=rpb devire la dle I b) pq,7r/:b b= prition du treions c) (ab)(pb)(bp) vrai (7(7pb))((7b7p)) cantrapose vrai (p>b)(bp) denieve la stite 2 vrai a faux v vrai faux U vrai vrai