So this happened to me during one of our local tournaments and this is the scenario:
Opponent has Void Ogre Dragon on field, I have Pot of Duality and A Hero Lives! in my hand, if I activate one and my opponent chooses to negate it, can the other card be activated still?? In other words, if I activate my Pot of Duality and he negates it, can I still activate A Hero Lives! ? And vice versa.