1. For these two problems related to the Island of Knights and Knaves, consider the propositional function K(x)"r is a knight", where the domain for r is all of the inhabitants of the Island. (a) While performing an academic survey on the Island of Knights and Knaves you manage to speak to every inhabitant on the island and each one tells you "Some of us are Knights and some of us i. Translate this statement into a predicate statement using quantifiers, connectives and K(x). ii. What can you conclude? Note that a truth table won't be much help because you don't know are Knaves" You may not define any other propositional functions how many people live on the island. Instead you should come up with a sensible argument (b) While performing a much lazier academic survey on the Island of Knights and Knaves you speak i. Translate this statement into a predicate statement using quantifiers, connectives and K(x) ii. What can you conclude? Again, do not use a truth table; a well-constructed argument will and justify it as concisely as possible. to only one inhabitant on the island and they tell you "All of us are Knaves" You may not define any other propositional functions. suffice