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3. let a h j p r s u denote...

Question: let a h j p r s u denote...

Question details

. Let A, H, J, P, R, S, U denote the following propositional variables: [6 points]

A : “The shark attacks Pat” R : “Jo rescues Pat.” H : “The shark is hungry.” S : “Pat goes swimming around the island ” J : “Jo is a knight.” U : “Swimming around the island is unsafe.” P : “Pat is a knight.”

Translate each of the following sentences into compound propositions using the above propositional variables, logical connectives, and parentheses when appropriate. Parentheses have been added to some sentences for clarification; otherwise, follow the conventions of precedence of logical connectives. Assume that Jo and Pat are inhabitants of the Island of Knights & Knaves.

(a) The shark attacks Pat only if the shark is hungry and Pat is a knave.

(b) A necessary condition for Jo to rescue Pat is that Pat goes swimming around the island whenever swimming around the island is unsafe .

(c) A sufficient condition for swimming around the island to be safe is that the shark is not hungry.

(d) Either Jo is a knight or the shark does not attack Pat.

(e) (If the shark attacks Pat, then Jo rescues Pat) unless Pat is a knave.

(f) Whenever the shark is hungry, Pat goes swimming around the island, but not conversely