This problem concerns languages over the alphabet ? = {1}. For any two integers q,r >0, define the language L1,q over as L1,q={1mati: m >0}={19,194.129+1,...}. For instance, L1,3 ={1,1111,1111111,...}. (a) Show that for every q and r, the language Ls,q is regular. (b) Show that if L is a regular language over , then L can be written as L = Ls1,9 UL12,9 U.--ULk,q u Lo, where 0 Srl <... are integers and lo is a finite set. this problem concerns languages over the alphabet for any two q>0, define the language L1,q over as L1,q={1mati: m >0}={19,194.129+1,...}. For instance, L1,3 ={1,1111,1111111,...}. (a) Show that for every q and r, the language Ls,q is regular. (b) Show that if L is a regular language over , then L can be written as L = Ls1,9 UL12,9 U.--ULk,q u Lo, where 0 Srl <... are integers and lo is a finite set>