Mark each of the following true or false.
___ a. Every G-set is also a group.
___ b. Each element of a G-set is left fixed by the identity of G.
___ c. If every clement of a G-set is left fixed by the same element g of G, then g must be the identity e.
___ d. Let X be a G-set with x1, x2 ∈ X and g ∈ G. If gx1 = gx2, then x1 = x2.
___ e. Let X be a G-set with X ∈ X and g1, g2 ∈ G. If g1x = g2x, then g1 = g2.
___ f. Each orbit of a G-set X is a transitive sub-G-set.
___ g. Let X be a G-set and let H < G. Then X can be regarded in a natural way as an H-set.
___ h. With reference to (g), the orbits in X under H are the same as the orbits in X under G.
___ i. If X is a G-set, then each element of G acts as a permutation of X.
___ j. Let X be a G-set and let X ∈ X. If G is finite, then |G| = |Gx| = |Gx|.
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