4. (Take-Home 2) Watermark insertion. Let W be finite singleton string representing a watermark. Given that some language L over the alphabet = {a,b} is regular, show that I' = {wiWw2|w1W2 L. W1, W2 *} is regular. (15pts) Repeat the above when the watermark is a set of strings L2 and is allowed to be split up. i.e. show that I' = {w181, W2 ... Sk-1 W2 where wiW2... Wk L1, S1 S2 ... Sk-1 L2, Wi, si e *} is regular . (15pts) 4. (Take-Home 2) Watermark insertion. Let W be finite singleton string representing a watermark. Given that some language L over the alphabet = {a,b} is regular, show that I' = {wiWw2|w1W2 L. W1, W2 *} is regular. (15pts) Repeat the above when the watermark is a set of strings L2 and is allowed to be split up. i.e. show that I' = {w181, W2 ... Sk-1 W2 where wiW2... Wk L1, S1 S2 ... Sk-1 L2, Wi, si e *} is regular . (15pts)