Exercise 1: (40 points) Prove that the following languages are Regular. Give the 5-tuple representation and draw the Finite State Automata that recognizes each language defined as: 1. L {we {0,1 }*: even number of 1 and even number of 0} 2. L(R) such that R=b(a UbUc)*a {Strings with symbols a bac that begin with a and end with a} 3. L(R) such that R= a*ba*b(ba*ba*b U a)* 4. L= {we {a, b}* : every b in w has one a immediately to its left and two as immediately to its right}. Example: &,q,aaa,abaa aabaa,abaabaa