Given the following grammar:

$SAB|C$

$A$aAb$|ab$

$BcBd|cd$

$C$aCd$|aDd$

$DbDc|bc$

$($a$)$ Draw a derivation tree $($parse tree$)$ for the string aabbccdd.

$($b$)$ Is the above grammar ambiguous? Yes or No$.$ Based on your answer,

you must prove it$.$