Given the following BNF Grammar, answer the following questions:

$->=$

$->$ A $|$ B $|$ C

$->+$

$|$

$->*$

$|$

$->()$

$|$

a$.(20$ points$)$ Show the parse tree of the following statements: A $=($ A $+$ B $)*$ C and A $=$ B $+$ C $+$ A

b$.(20$ points$)$ Show the left$-$most derivation of the following statements: A $=($ A $+$ B $)*$ C and A $=$ B $+$ C $+$ A

c$.(10$ points$)$ Add more rules to the given BNF grammar to make it generate statements with $-$ and $/$ operators as well.