a$)$ Eliminate all epsilon rules in the following grammar:

A $|$ xAy $|$ AA

$SSa|aSSSb|$

b$)$ Eliminate left recursion in the following grammar:

$AAb|$ aC

$B$BaBB$|BA||$

$CbC|$ BA

c$)$ Eliminate left recursion in the following grammar:

$T$ Txxy $|$ TaabT $|$ TTa

d$)$ Eliminate left recursion in the following grammar:

$ABa$ I Baa

$BAb|$ Abb

e$)$ Eliminate left recursion in the following grammar:

$SAa|Bb$

$AAa|$ Abc $|$ c $|$ Sb

$Bbb$