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be sure to give at least a brief explanation or justification for each claim that you make. (1). [5 points] (Refer to Problem 1.16, Devadoss-O'Rourke.) (a). For the polygon below, find the number of distinct triangulations. Show your work, explaining your answer. (b). Draw two different simple polygons

`P`

and

`Q`

, each having exactly 4 different triangulations, while having different numbers of vertices, convex vertices, and reflex vertices. (i.e.,

`n(P)!=n(Q)`

,

`c(P)!=c(Q)`

, and

`r(P)!=r(Q)`

, where

`n(P),c(P)`

, and

`r(P)`

denote the number of vertices, the number of convex vertices, and the number of reflex vertices of polygon

`P`

). State clearly what the values of

`n,c`

, and

`r`

are for each example, and justify (briefly) why they each have exactly 4 different triangulations.