Reference no: EM131570682

Question: Let P (n) be the statement that when nonintersecting diagonals are drawn inside a convex polygon with n sides, at least two vertices of the polygon are not endpoints of any of these diagonals.

a) Show that when we attempt to prove P (n) for all integers nwith n ≥ 3 using strong induction, the inductive step does not go through.

b) Show that we can prove that P (n) is true for all integers n with n ≥ 3 by proving by strong induction the stronger assertion Q(n), for n ≥ 4, where Q(n)states that whenever nonintersecting diagonals are drawn inside a convex polygon with n sides, at least two nonadjacent vertices are not endpoints of any of these diagonals