$2.$ Given a language L$=($we $($a$,$ b$)$ the number of a$\text{'}$s in w is twice the number of b$\text{'}$s$).$

a$.$ Design a context$-$free grammar $($CFG$)$ that generates this language. Provide the set of production rules, non$-$terminal symbols, terminal symbols, and the start symbol for the CFG$.(10$ Points$)$

b$.$ Remove ambiguity using Chomsky Normal Form $($CNF$)$ from the production rule of the grammar L$.(10$ Points$)$

Construct a push down automata for the CFG in question $2.$a $(10$ points$)$