1. (20 points) Suppose that A, B, and C are regular sets. AB is the nor operator. ABC is defined as
A|BC ={x|x is in neither A nor B nor C}
(a) Using logical operations, show that ABC is a regular set.
(b) By constructing a machine M that accepts ABC when A, B, and C are regular sets show that ABC is a regular set. (Hint: Think about the machine that we constructed to show that the family of regular sets is closed under set intersection.)