Please explain how the second De-Morgan Law can be applied to solve Strange Isla
ID: 3647062 • Letter: P
Question
Please explain how the second De-Morgan Law can be applied to solve Strange Island problem.Strange Island Problem: Somewhere in the vast reaches of the ocean, there is a very strange island known as the Island of Questioners. It derives its name from the fact that its inhabitants never make statements, they only ask questions. The inhabitants ask only questions answerable by Yes or No. Each inhabitant is one of two types, A and B. Those of type A ask only questions whose correct answer is Yes; those of type B ask only questions whose correct answer is No. For example, an inhabitant of type A could ask, "Does two plus two equal four?" But he could not ask whether two plus two equals five. An inhabitant of type B could not ask whether two plus two equals four, but he could ask whether two plus two equals five.
I once visited this island and met a couple named Ethan and Violet Russell. I heard Ethan ask some, one, "Are Violet and I both of type B?' What type is Violet?
Explanation / Answer
Case I: Say Ethan is of Type A.
Truth: Violet & Ethan are both of Type B.
Contradicted.
Case II: Say Ethan is of Type B.
Truth: ~ (Violet and I are both of Type B)
=> ~(Violet is of Type B) or ~(Ethan is of Tpe B)
[According to Second DeMorgan's Law]
=> (Violet is of Type A) or (Ethan is of Type A)
Since Ethan is already of Type B, Violet shoud be of Type A.