Let (P, E) be a projective plane. (a) Prove that if E is regarded as the set of points and P is regarded as the set of lines, then the structure (E, P) is also a projective plane (called the \\emph{dual} of (P, E)). (b) Suppose there exists a line a,\" E E which is on exactly n + 1 points. Show that every line a,\" e E is on exactly n + 1 points. (c) Show that if some line a,\" E E is on exactly n + 1 points, there the projective plane has exactly rt2 + n + 1 points and exactly n2 + n + 1 lines