Please answer for all 3 choices.

In this problem, you will use the Pumping Lemma to show that L={w {0,1,2) * ||wlo:lwl, =lw2}is not regular. Note that this language consists of all strings in {0,1,2} * where the number of Os times the number of ls equals the number of 2s and the order of these symbols does not matter. The adversary picks n > 0. o Your opponent picks some integer n. You pick W E L such that|wl2n. o Which one of the following is a good choice for w? a. w=2"1"0" b. w=2"1"02 C. W=2"1","2 a b The adversary picks x,y,z {0,1,2}* with w=xyz, y # , and|xy| sn. o Which one of the following must be y? a. y=0', o 0 such that xyz L. o Assume that you pick k = 2. Why does xy22 L? a. xy2z=2" + 1"0", (n+i)nen b. xy2z=2" + 1"02", (n+i)n # 2n C. xy2z=2" + 1"o"? (n+i)n6n2