It is possible for two different finite languages X and Y to have the same Kleene star, that is$,$forX $=$Y tobetrue.$($a$)$ ProvethatX $=$Y ifandonlyifbothXY andY X$.($b$)$ Usepart$($a$)$toshowthatX $=$Y ifX$=\{$a$,$abb,bb$\}$andY $=\{$a$,$bb$,$bba$\}.($c$)$ ProvethatifX $=$Y$,$XY$,$wisanystringofminimumlengthinX,andzis any string of minimum length in Y $,$ then w and z have the same length.