Part $2$: Pump It Up

Using the pumping lemma, prove that each of the following languages are not regular.

a$.$ where $f,g,$ and $h$ are integers in binary, and $h$ is the sum of $f$ and $g$

Note that the alphabet here is $\{0,1,+,=\}.$

$($One interpretation of this result is that DFAs can't do addition.$)$

b$.L_2=\{\begin{array}{ccc}\text{x}\text{i}\text{n}& \{a,& b{\}}^{*}|x\end{array}$ is a palindrome