$1)$ Consider the following grammar in BNF $=$ A $|$ B $|$ C $+<$ expr$>|*|()|$ Using the grammar defined above, show a parse tree and a leftmost derivation for the following statement: A$=$ A$*($B $+($C $*$ A$))2)$ Consider the following grammar in BNF $->=->$ A $|$ B $|$ C $->+|->*|$ factor $->()|$ Rewrite the grammar to give $+$ precedence over $*$ and force $+$ to be right associative. $3)$Prove that the following grammar is ambiguous. $->->+|->$ a $|$ b $|$ c $4)$ Convert the following BNF into EBNF $=$ A $|$ B $|$ C $+<$ expr$>|*|()|$