1. Consider the expression R1 = (a+ab) . Consider also R2 = (a+ba).

a) Describe the languages L(R1) and L(R2) in words.

b) Can you find a regular expression for L(R1) L(R2)? How about L(R1) \ L(R2) ? Use the descriptions in words to carefully justify your answers.

c) Now consider the regular expression R3 = (b+ab) . Find a regular expression for L(R1)L(R3), again, using your characterization in words to derive and justify your answer.