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 element 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|.