Let F denote the projective plane of order 4. (a) How many points are there in F? (b) How many lines are there in F? (C) For each point P of F, how many lines of F pass through P? (d) Let S denote the sentence Each point is incident with at most four distinct lines." Explain why S is not a theorem of Projective Geometry (PG). (e) Explain why S is independent of PG. Let F denote the projective plane of order 4. (a) How many points are there in F? (b) How many lines are there in F? (C) For each point P of F, how many lines of F pass through P? (d) Let S denote the sentence Each point is incident with at most four distinct lines." Explain why S is not a theorem of Projective Geometry (PG). (e) Explain why S is independent of PG