Background For any three regular expressions a, b, and y, the following properties hold: 1. Commutativity of union: a + B = 3 + a 2. Associativity of union: (a +B) +7= a + (+7) 3. Associativity of concatenation: (a)= a(BY) 4. Distribution of union: a(+7)= a + ay and (+7)a = Ba +ya. 5.0 is the identity element for union: a +0=a. 6. ) is the annihilator element for concatenation: a) = Da = 0. 7. e is the identity element for concatenation: ae = a. 8. Idempotence of Kleene star: q** = q* Problems 1. The regular expression a = (0110+01)(10)* can be written in a more simplified way. a. [10 points] By reasoning based on L(a), define a shorter regular expression equal to a. Explain your reasoning. b. (10 points] Using the properties explained above, prove that the expression you came up with in (a), is indeed equal to a