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.