Answer the following questions.

$($a$)$ List the productions that violate the conditions of the Chomsky Normal Form $($CNF$)$ in the following gram$-$

mar

$S_{0}S|$

$SAB$

$AAS|aAb$

$BB{S}_0|$

$($b$)$ Write down the additional rules that need to be added to the following grammar if the production $A$ is

removed.

$S$aABA$|A$

$A$ABAB$|$

$B$BAb$|bBABb$

$($c$)$ Write down the additional rules that need to be added to the following grammar if all the unit productions

are removed.

$Sxa|Yb$

$xY|ZZ|ax$

$YxY|Zb|x$

$Z$ZaZ$|Zx|Zxx$