Given grammar: S $->0$ S $1|$ epsilon L$($G$)=\{0^$x $1^$x $|$ x $>=0\}$

$0$s are followed by the same number of $1$s and the shortest string is empty.

S $=>0$ S $1=>00$ S $11=>000$ S $111=>000111$

Refer back to this grammar to answer Q$1$ and Q$2.$

Q$1.$ My L$($G$)=\{0^$x c $1^$x $|$ x $>=0\}$

a$.$ Describe the language in English without referring to x$.$ Also state the shortest string. $?**?$

b$.$ Change the above grammar to generate this language. $($a very minor change$)?**?$

Q$2.$ My L$($G$)=\{0^$x $1^$x c $0^$y $1^$y $|$ x $>=0$ and y $>=0\}$

a$.$ Describe the language in English without referring to x$.$ Also state the shortest string. $?**?$

b$.$ Change the above grammar to generate this language. $($This is NOT S $->0$ S $10$ S $1)?**?$

Q$3.$ What is L$($G$)$of the following grammar?

Give a set former description as done above for the following. $?**?$

S $->0$ B $1$ HINT: At least how many $1$s$???$

B $->1$ B

B $->1$