Please I need you to solve it step by step with proper and complete diagrams.

a$.$ Consider the following Context Free Grammar with nonterminals A and $B,$ and terminal symbols: $\text{'}x\text{'},$

$\text{'}y\text{'}$ and $\text{'}z\text{'}$:

$A$ABA$|z$

$BB|yx$

i$.$ If A is the starting symbol, then the string $"$zxxyyxz$"$ can be derived from this context$-$free

grammar. Give three other strings which can also be derived.

ii$.$ Explain what is meant by the term "left$-$recursive context free grammar" and explain

whether the CFG given above is left recursive.

iii. Draw a parse tree for the following string which can be derived by the above CFG:

zxyyyxz

b$.$ Consider the following NFA over alphabet $\{a,b\}$ :

i$.$ Identify the start and final state$($s$)$ of the NFA.

ii$.$ Construct a Deterministic Finite Automaton $($DFA$)$ which is equivalent to the NFA by using

the subset construction.