(i) Explain why we can take any pair of equivalent regular expressions and replace the letter a in both with any regular expression R and the letter b with any regular expression S and the resulting regular expressions will have the same language. For example, 16(ii), which says

(a*b)*a* = a*(ba*)*

becomes the identity

(R*S)*R* = R*(SR*)*

which is true for all regular expressions R and S. In particular, R = a + bb, S = ba* results in the complicated identity

((a + bb)*(ba*))*(a + bb)* = (a + bb)*((ba*)(a + bb)*)*

(ii) What identity would result from using

R = (ba*)* S = (Λ + b)