$5.$ Consider a logic equation with three input variables, y $=$ f$($a$,$ b$,$ c$).$ For each expression below, identify it as being a properly formed i$)$ sum term, ii$)$ maxterm, iii$)$ product$-$of$-$sums, iv$)$ product$-$of$-$maxterms, or v$)$ none of these. Some expressions should identify as multiple forms. $(20$ points$)$

a$.$ a $+$ b$+$ c

b$.$ b$($a$+$c$)$

c$.$ a$$bc$$

d$.($a$+$b$+$c$)($a$+$b$+$c$)+($a$+$b$+$c$)$

e$.($a$+$b$+$c$)($a$+$b$+$c$)($ab$+$c$)($a$+$b$+$c$)$