Problem $2$:

A grammar G is formally defined as a $4-$tuple $($V$,\backslash$Sigma $,$ R$,$ S$),$ where:

$$ V is a set of variables $($non$-$terminal symbols$).$

$\backslash$Sigma is a set of terminal symbols.

$$ R is a set of production rules.

$$ S is the start symbol.

Given the grammar below, identify the $4-$tuple components V$,\backslash$Sigma $,$ R$,$ and S:

Grammar:

$1.$ S $->$ aA $$ bB

$2.$ A $->$ aS $$ bAA

$3.$ B $->$ bS $$ aBB

$4.$ A $->$

$5.$ B $->\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$