$1.$Compute First sets to determine if LL$(1).$ Show your work in detail showing what sets you use and how and how this leads to your decision.

A $->$ daB $|$ Ba $|$ a

B $->$ b $|$ c

$2.$Given the grammar below, without any modifications, is it LL$(1)$ in its current form and why yes or no$?$ Show your work.

If not LL$(1),$ rewrite as using left$-$factorization LL$(1)$ and verify it is $($do the same all over$).$

S $->$ abCS $|$ AC

A $->$ bA$|$bc $$

C $->$ cC $|$ D

D $->$ dd$$