I will like to ask where are these (xyz,xyw,xzw,yzw)come from and how to get these four tuples. Pls see what I done and answer the question what I am asking

where one these X come from ? e the first s that "x always b these Question 4. For each society we must check four tuples, (xyz, xyw, xzw. yzw) one ? where ane reperesend ? to determine if at least one outcome satisfies value restriction, i.e. is agreed to Analyzing Politics be either not best, not middle or not worst by all members. *5. For each of the following societies, state whether the pref- erences satisfy Sen's value-restriction criterion, that is, that for any three outcomes, all voters agree that at least one of (1) Society 1: the preference does not satisfy Sen's value restriction criterion. the outcomes is not first, middle, or last. If not, identify the tuple(s) of preferences that violate value-restricted prefer- ences. Assuming that the voting rule is majority rule, are the y is agreed to be not worst among xyz; r is agreed to be not best among ryw; group preferences in societies without value-restricted prefer- ences transitive or intransitive? There fore, no option satisfies value restriction among xzw; and y is agreed to be not worst at these one of among yzw. Society 1: No x w y x is not the best y PixP z P, w y is not the last. w P, y P, x P, z w > y y x y z w ysx y wit z P3 y P3 W P3 x q q y > W x x . wxy 10 win z 2 win = > w > y y x Using the method of majority rule, there is preference cycle among x, z and w. 3 win Society 2: Busx x win condercent rule . x yz x ,W y therefore not y P, wP zP x yaws ZZz . *Is agree not to value - restrict ed (2) Society 2: the preference satisfies Sen's value restriction criterion. w P, x P, y P, z be the best . preferences. y is agree not to z P3 W P3 y P3 x be the last . yush w vs * " win No 3 15 W Society 3: $ win y > Z Y W y x y is agreed to be not worst among xyz; w is agreed to be not worst among ryw; W Z x y y win this don't have condercent cycle . y P, wP zP x yo w y z y x It is value- restricted w is agreed to be not worst among czw; and z is agreed to be not middle among 2 > x x y SW preference . z P, xP, y P, w yzw. (Using the method of majority rule, there are no preference cycles in this x P3 y P3 w Paz y usw y win society, as predicted by Sen's value restriction theorem.) . wis agree not to wy Z z x > y > w be the best 8 US x Z win y is agree not to busy * win . condercent cycle . be the last . wus x x win (3) Society 3: the preference does not satisfy Sen's value restriction criterion. Wus win N I - So where to No outcome satisfies value restriction among xyz; x is agreed to be not middle get these and how? V . in amonod +