In Exercises 8 and 9, show that the given set of axioms is inconsistent.

8. (i) There are exactly four points in the system.

(ii) Each pair of points lies on exactly one line.

(iii) Every line contains exactly three points.

9. (i) There is at least one line in the system.

(ii) Every two points lie on exactly one line.

(iii) Every point lies on exactly two distinct lines.

(iv) Every line contains exactly three points.

10. Explain why the following statement is a paradox: This sentence is false.

11. Suppose there are two types of people living on a certain island: truthtellers (who never lie) and liars (who never tell the truth). a) An inhabitant of the island says, I am lying. Explain the paradox. b) An inhabitant of the island says, You will never know that I am telling the truth. Is this a paradox?