Suppose you meet three inhabitants A, B, & C of Smullyan's Island

Question

Suppose you meet three inhabitants A, B, & C of Smullyan's Island. Let p represent the statement" A is truthful", q represent the statement" B is truthful", and r represent the statement" C is truthful". Write each of the following in symbolic logic notation: i. At least two people are telling the truth. ii. Exactly two people are telling the truth.

Answer 1

Start by writing out in sentences the conditions that are being asked.  That is:

i: (A is truthful and B is truthful) or (A is truthful and C is truthful) or (B is truthful and C is truthful)

Note that in each "and" statement, we only need two people to be be truthful.

For the second part you have to include the above possibilities but also add in the negation of the third person being truthful.  One of them might be: p & q & ~r.   

Hope this helps :)