Let G = (G, . , e), H = (H , * , E) be groups ... (e is the identity) the direct product is defined by: G x H = (GXH, o , (e,E)) where, (g1,h1) o (g2,h2) = (g1 . g2, h1*h2) Question: Show formally that G x H is a group. when it says, "show formally that G x H is a group".. does it mean show that G x H satisfies the 4 conditions for being a group.. i.e. associativity, closure, existance of identity element and existance of inverse element? any help is appreciated..