a$.$ Prove: If L is finite $($has a finite number of strings$)$ then L is regular.

b$.$ Prove: If L$1$ and L$2$ are both regular, then so is L$1\backslash$cap L$2.($You could take the DFAs$/$NFAs$/$regular

expressions for the two languages and try to combine them. But there isn$$t any easy way to do that. The

easy proof for this uses deMorgan$$s laws. Rewrite L$1\backslash$cap L$2$ and use theorems $1\mathrm{.}25,1\mathrm{.}45-1\mathrm{.}49)$