Context Free Grammars

Consider the following Grammars:

Grammar $1$ Grammar $2$ Grammar $3$ Grammar $4$

$SAB,S$ASB$|a,SSc|AB,S$ASB$|cScc|c$

$A$aAa$|a,AaA|a,AaA|a,A$aaA$|a$

$BbBbb|lon,BbbB|c,BbbB|b,BbbB|b$

$($a$)$ Which grammars $($of $1,2,$ and $3)$ accept both "aabbbbc" and "aaabbcc"? Select all

that apply. $()$

A$.$ Grammar $1$

B$.$Grammar $2$

C$.$Grammar $3$

D$.$ None

$($b$)$ Ambiguity $(9$ points$)$

"aaabbb" is an ambiguous string in Grammar $1$

"aaabbc" is an ambiguous string in Grammar $2$

"aaabcc" is an ambiguous string in Grammar $3$

$($c$)$ Which strings are accepted by Grammar $4?$ Select all that apply. $(5$ points$)$

A$.$ aaacbbb

B$.$ aaacbbbb

C$.$ ccaaabbbbcc

D$.$ cacacbbbb

E$.$ None