Three chests lie before you. Each chest will either only tell the truth or lie. Only one chest

will contain gold.

Chest $1$: The gold is in this chest.

Chest $2$: The gold is not in this chest.

Chest $3$: The gold is not in chest $1.$

Use the following to help formulate proof of who is telling the truth and where the gold is$.$ A

closed system is one in which the result is concluded. You will convert the logical statements into

a Boolean algebraic expression, whose result should be $1$ to prove your findings. x$=$ starting point conditions met y$=$ hypothesis q $=$ conclusion Lets tie in the propositions so that they form a closed system: x AND $($if p then q $)$ logical statement a$.$ Define the variables, atomic propositions, and quantifiers as logical representations.

b$.$ Use the quantifiers to simplify and build atomic propositions $($you might need some xors$)$ in

terms of logical representation.

c$.$ What is the complex statement we intend to prove?

d$.$ Create new variables for your three propositions obtained to describe the $3$ chests, then

write a boolean expression in the form $z=1$ in terms of $x$ and $y.$ You should be able to arrive

to this based on proper construction of proposition statements for the $3$ chests.

e$.$ Simplify the boolean expression above and justify steps, this will help you determine the

value for $y,$ which you can use to rationalize $x.$

f$.$ Based on the answer in e$,$ determine where the gold is$.$

g$.$ Present the overall proof.