Only need question 3 answered. the other parts are just examples of how to format the answer

Example:

Only need question 3 answered. the other parts are just examples of how to format the answer

3. (15%) Suppose that L is CF and R is regular. Show that the following language is CF. L = {U1.V1 ..... Uk Uk k>0, Wi E L, vi & R} P3. Suppose that L is a CFL and R a regular language. Show that (LU-R)* is a CFL. Solution. Since R is regular, R is also regular, and therefore CF. The collection of CFL's is closed under union and star, so (LU-R)* is CF. 3. (15%) Suppose that L is CF and R is regular. Show that the following language is CF. L = {U1.V1 ..... Uk Uk k>0, Wi E L, vi & R} P3. Suppose that L is a CFL and R a regular language. Show that (LU-R)* is a CFL. Solution. Since R is regular, R is also regular, and therefore CF. The collection of CFL's is closed under union and star, so (LU-R)* is CF