Answer the following, include diagrams if required.

3. Let be any alphabet and let A,B be given regular languages. (a) Define a language C as follows: C={uxv:u,x,v,uvA,andxB}. In words, C is the language of all strings that can be obtained by first choosing a string from A and then inserting anywhere into that string any one string chosen from B. Prove that C is regular. (b) Define a language D as follows: D={uv:u,x,v,uxvA,andxB}. In words, D is the language of all strings that can be obtained by first choosing a string from A and then removing from that string any one substring that is contained in B. Prove that D is regular. Hint: you do not actually need to use the assumption that B is regular to conclude that D is regular