Let H and K be groups and let G = H X K. Recall that both H and K appear as subgroups of G in a natural way. Show that these subgroups H (actually H X {e}) and K (actually {e} X K) have the following properties.
a. Every element of G is of the form hk for some h ∈ H and k ∈ K.
b. hk = kh for all h ∈ H and k ∈ K. c H ∩ K= {e}.
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