[18 points] Consider the alphabet E = {0, 1, a, b}. We say two strings u, v E E* are equivalent, denoted by u = v, if (i) [u] = [v], and (ii) V1 [u], ((U; E {0, a} \ V; E {0, a}) V (U; E {1, b} A V; E {1, b})). For example, 0 = a,00b = a01, and 006 abl. We define the equivalence relation R on a set S CE* as follows: Vu, v E S, (uRv + u = v). 1. List all the elements in the equivalence class [Oal] that is defined by R on *. 2. How many elements are in the equivalence class [aObla0b11] that is defined by R on 2* ? Explain. 3. Let Sn = {u ES: Jul [u], ((U; E {0, a} \ V; E {0, a}) V (U; E {1, b} A V; E {1, b})). For example, 0 = a,00b = a01, and 006 abl. We define the equivalence relation R on a set S CE* as follows: Vu, v E S, (uRv + u = v). 1. List all the elements in the equivalence class [Oal] that is defined by R on *. 2. How many elements are in the equivalence class [aObla0b11] that is defined by R on 2* ? Explain. 3. Let Sn = {u ES: Jul