6.11. (a) Prove that G acts transitively on X if and only if there is at least one xX such that Gx=X. (See Definition 6.20 for the definition of a transitive action.) (b) Prove that G acts transitively on X if and only if for every pair of elements x,yX there exists a group element gG such that gx=y. (c) If G acts transitively on X, prove that #X divides #G. 6.11. (a) Prove that G acts transitively on X if and only if there is at least one xX such that Gx=X. (See Definition 6.20 for the definition of a transitive action.) (b) Prove that G acts transitively on X if and only if for every pair of elements x,yX there exists a group element gG such that gx=y. (c) If G acts transitively on X, prove that #X divides #G