For languages (sets of strings) A and B, the three operations are defined as follows. 1. Union: AU B = {x|x A or x E B} 2. Concatenation: AB = {xy|x e A and x B} 3. Star: A* = {X1X2 ... Xn]n e N and xi E A} Suppose there are the following 4 languages over the alphabet {a,b}, 1) L={a}* U {b}* 2) L2={a} {b}* 3) L3={ab, ba* 4) L4={a, b) U aa, bb} For each language, answer the following questions: (1) Is (the empty string) in the language? (2) What is an example of a string over {a, b} of length at least 2 that is in the language (if there is no such string, explain why)? (3) What is an example of a string over {a, b} of length at least 2 that is not in the language (if there is no such string, explain why)