Let X be a finite set. Check whether the following three choice correspondences, defined overall non-empty subsets of X, satisfy WA:

C(A) ={xA| the number of yX for which V(x)V(y) is at least |X|/2}, and if the set is empty, then C(A) =A.

D(A) ={xA| the number of yA for which V(x)V(y) is at least |A|/2} E(A) = {xA|x>=1 y for every yA or x>=2 y for every yA} where>=1and >=2 are two strict preferences over X.