Question

Verify the following identities involving regular expressions.

e) (r s)t = rt st.
g) (e r)* = r*.
A) (r s)t = t(r s)
B) (r s)t = r(st)
C) (e r)* = e*(r*)
D) (e r)* = re

Answer 1

To verify the given identity, we analyze the regular languages represented by both sides of the equation and show that they are equal.

Step-by-step explanation:

To verify the identity (r s)t = rt st, we need to show that both sides of the equation represent the same regular language. Let's start by defining the regular languages represented by the left and right sides.

Left side: (r s)t

Right side: rt st

Now, let's analyze each side separately to check if they represent the same language.

Left side: (r s)t

1. The expression (r s) concatenates the languages represented by r and s.
2. The expression (r s)t concatenates the language represented by (r s) with t.

Right side: rt st

1. The expression rt concatenates the languages represented by r and t.
2. The expression rt st concatenates the language represented by rt with st.

Since both sides of the equation involve concatenation operations, we can conclude that (r s)t = rt st.