3. (10 points) a) Consider the true statements: If A and B are regular languages then AnB is regular - There exist context-free languages A and B such that An B is not context-free Explain why the statement from problem 2; "If L is a context-free language and K is a regular language then LnK is context-free." does not contradict each of these bullet points. b) Find languages AS BSCSDS E all over the alphabet a, b, c such that: - A is not context-free - B is context-free and non-regular - C is regular - D is non-regular E is regular and not (a,b,c Briefly justify the subset inclusions and either prove or cite examples in the book to explain why you chose each set