$7)$ A landfill is the cheapest method of solid waste treatment and disposal. Once disposed into a landfill, solid waste can be a major source of energy due to its methane at the same rate and in the same quantities. Based on its biodegradability, solid waste is classified into three distinct groups, namely, rapidly biodegradable, moderately biodegradable, and slowly biodegradable. Design of a landfill gas extraction system is based on gas production through the first two groups; both have different gas production patterns. The data collected from experiments and experiences are presented by the sets $\backslash ($ A$\_\{1\}\backslash )$ and $\backslash ($ A$\_\{2\}\backslash )$ as shown in Figure below, where $\backslash ($ A$\_\{1\}\backslash )$ and $\backslash ($ A$\_\{2\}\backslash )$ are defined as the fuzzy sets rapidly biodegradable and slowly biodegradable, respectively, in units of years.

a$)$ Discuss the properties of the membership functions of $\backslash ($ A$\_\{1\}\backslash )$ and $\backslash ($ A$\_\{2\}\backslash )($Core$,$ Support, Boundary, Crossover point, height$)$

b$)$ Discuss the classification of fuzzy sets $\backslash ($ A$\_\{1\}\backslash )$ and $\backslash ($ A$\_\{2\}\backslash )($Convex$-$Nonconvex, NormalSubnormal$).$