Answer a and b

Question 4 ( /2 marks) In the back of an old cupboard, you discover a note signed by a pirate famous for his bizarre sense of humour and love of logical puzzles. In the note he wrote that he had hidden a treasure somewhere on the property. He listed five true statements and challenged the reader to use them to figure out the location of the treasure. 1. There is a large rock either on the hill or near the lagoon. 2. If there is a shipwreck on the beach, then the treasure is buried under a tree. 3. Either there is a no shipwreck on the beach, or the treasure is hidden in a cave. 4. If there is a large rock on the hill, then there is no shipwreck on the beach 5. There is no large rock near the lagoon. Assume the word or in instruction 1 refers to non-exclusive or (disjunction) while the use of "Either... or in instruction 3 refers to exclusive or. This question has two parts, each worth 1 mark. a) Translate the five true statements in the pirate's note to propositional logic. Be sure to clearly define all atoms used. b) Could there be a treasure? If so, where could it be hidden and what truth values did you assign to each atom to find it? If there cannot be a treasure, justify your