Question

You find the following puzzle left by a famous pirate:

1. If my parrot's name is not Lago or the treasure is not in the lagoon, then we drank a barrel of rum in one sitting.
2. The treasure is in the lagoon or sunk on the coral reef.
3. If the treasure is sunk on the coral reef, then we did not drink a barrel of rum in one sitting.  
4. If our ship came to this island on a stormy night, then let it be known: the treasure is not in the lagoon or we did not drink a barrel of rum in one sitting.
5. If my parrot's name is Lago, then our ship did not come to this island on a stormy night ".
6. You know this pirate's story well enough to remember that his parrot's name was Flint, not Lago.

In this question, you need to use logic (namely, natural deduction) to solve this puzzle (that is, determine where the treasure must be for the sentences in the puzzle to be true). You can translate everything to logic formulas, or do your derivation in English, but do show your steps (you can use numbers for sentences, and number derived sentences to refer to them later). If assigning variables to propositions, assign them in the order in which they appear (eg, A: "Parrot's name is Lago"). In case you would like to use symbols, here they are: ∧ ∨ ¬ → ↔ ∴   

Answer 1

1] If {Parrot != Lago} OR {Treasure!=Lagoon} -> {Barrel of Rum}

2] Treasure = {Lagoon, Coral Reef}

3] {Treasure = Coral Reef} -> {!Barrel of Rum}

4]{Stormy night} -> {Treasure != Lagoon}

5]{Parrot != Lago} -> {!Stormy Knight}

Given : Parrot = "Flint" -> {Parrot != Lago} = TRUE

Therefore, statement 1 becomes TRUE OR {Treasure!=Lagoon} -> {Barrel of Rum}

Thus, {Barrel of rum} = TRUE

In statement 3, if {Treasure = Coral Reef}, then {Barrel of Rum} = FALSE

We know that {Barrel of Rum} = TRUE,

thus {Treasure != Coral Reef}

Since Treasure can only be in {Lagoon, Coral Reef}, it must be in the Lagoon.

Please let me know if any specific part was confusing.