Question

We defined the operation of concatenation for sets of strings on p. 10, AB = { XY | X ∈ A and y ∈ B}Are the regular sets closed under concatenation? That is, if A and B are regular sets, is AB guaranteed to be a regular set? Prove or show a counterexample.

Answer 1

Answer and Explanation:

Solution: The operation of concatenation for a set of string on p. and the set is

     AB = {XY | X ∈ A and y ∈ B}.

We need to satisfy all these following properties to find out the standard set is closed under concatenation.

1- Union of two standard sets also belongs to the classic collection. For example, A and B are regular. AUB also belongs to a regular group.

2- Compliment of two standards set A and B are A’ and B’ also belonging to the standard set.

3- Intersection of two standards set A and B is A∩B is also a regular set member.

4- The difference between two regular sets is also standard. For example, the difference between A and B is A-B is also a standard set.

The closure of the regular set is also standard, and the concatenation of traditional sets is regular.