Answer to Question #188722 in Discrete Mathematics for afzal

Question

An island has two types of inhabitants. Those of type A
only ask questions whose correct answer is Yes. Those of Type B
only ask questions whose correct answer is No. On the Island, you
encounter Tom and Jerry who are inhabitants of the island. Tom asks
“Are Tom and Jerry both of Type B”. Determine the types of Tom and
Jerry. Justify your answer.

Answer 1

Case I: Say Tom is of Type A.

Truth: Tom & jerry are both of Type B.

Contradicted.

Case II: Say Tom is of Type B.

Truth: ~ (Jerry and I are both of Type B)

=> ~(jerry is of Type B) or ~(Tom is of Tpe B)

[According to Second DeMorgan's Law]

=> (jerry is of Type A) or (Tom is of Type A)

Since Tom is already of Type B, Jerry shoud be of Type A.