Question

1. 5 points Let G, H, J, and P denote the following propositional variables: G: "Jo knows where the gold is hidden." J : "Jo is a knight." H: "Pat knows where the gold is hidden." P: "Pat is a knight." One fine day, while we are strolling along on The Island of Knights & Knaves, we meet Jo and Pat, each of whom is an inhabitant of The Island of Knights & Knaves Jo says "We both know where the gold is hidden if and only if at least one of us is a knight." Pat says "Neither of us knows where the gold is hidden, but I am a knight." la. Translate each speaker's statement into propositional logic using the above variables, appropriate logical connectives, and parentheses wherever needed Jo says: Pat says: 1b. What can you conclude? State all possibilities and be specific about Jo's type, Pat's type, and whether or not they know where the gold is hidden. Show your work and explain your reasoning! Bonus Q1* [+2 points] Suppose later that day Pat makes a second statement to us. Pat says: "A sufficient condition for me to be a knight is that 2 2-5. What more (if anything) can you conclude now? Be as specific as possible. You do not need to show your work for this bonus question. Simply circle the correct answers below: Regarding Jo's type: Regarding Pat's type: Regarding where the gold is hidden Jo... knows does not know It is impossible for us to determine this. Regarding where the gold is hidden P... knows does not know It is impossible for us to determine this. Jo is a... knight knave It is impossible for us to determine this. Pat is a.. knight knave It is impossible for us to determine this.

Answer 1

AL aia b). Pal a Knaw. Valid. an