A finite projective plane PG(2,3) of order 3, can be defined as follows: The points are elements of the ring Z13 := {0,1,...,12}where these are taken modulo 13 (the remainder when an integer is divided by 13). Let D be {0,1,3,9} CP:= Z 13 and let the lines be subsets gi:= i +D (mod 13). Don't draw the whole structure PG(2,3)! Writing down all the lines as sets is possible. (9) Find a formula in terms of the function f for the line that contains two distinct points i andj. Use this to show that any pair of distinct points are on a unique line. (h) Show that there are 3 points of PG(2,3) that are not collinear. (This is the last step in showing that the structure is a projective plane.) A finite projective plane PG(2,3) of order 3, can be defined as follows: The points are elements of the ring Z13 := {0,1,...,12}where these are taken modulo 13 (the remainder when an integer is divided by 13). Let D be {0,1,3,9} CP:= Z 13 and let the lines be subsets gi:= i +D (mod 13). Don't draw the whole structure PG(2,3)! Writing down all the lines as sets is possible. (9) Find a formula in terms of the function f for the line that contains two distinct points i andj. Use this to show that any pair of distinct points are on a unique line. (h) Show that there are 3 points of PG(2,3) that are not collinear. (This is the last step in showing that the structure is a projective plane.)