Part I: Using rules of inference for p ropo3 There is an island that has two kin

Question

Part I: Using rules of inference for p ropo3 There is an island that has two kinds of inhabitants: knights, who always tell the truth, and knaves who always lie. You encounter two inhabitants of the island, A and B. A says: "I am a knave, but B isn't." What are A and B? Let p be the statement A is a knight and q be the statement 'B is a knight (5 pt.) Assume that A is a knave. Write your hypotheses in terms of p and q. Then, use the rules of inference to determine whether B is a knight or a 1. knave. n twa rooms, each of which contains either a lady or a tiger. There is in in this room or a lady is in the other room fnlse Which room

Explanation / Answer

p : A is a knight.

or

~p : A is a knave.

q : B is a knight.

or

~q : B is a knave.

Suppose, A is a knave.

~p => T

Now, what A says must be false.

That means, ~p ~q ó F (false)             -> Statement 1

So, ~p ~q ó T ~q ó T (always)   -> Statement 2

It can be seen that the Statement 1 and statement 2 are contradictory in themselves which isn’t possible.

Hence, A is a knight and is telling the truth.

Then,

p

¬p ¬q

----------------

¬q

Then, from the derived expressions at the top, it can be justified that ‘B’ is a knave, when ‘A’ is a knight.

Hence, proved.

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