Is it bad for a parent to let their young on play violent video game and let them watch violent tv shows

Not if the parent is there to give the violence context. The world is a violent place, and kids need to be aware of this, lest it take them by surprise when they're older. We can avoid this by exposing them to violence at younger ages, as long as the child understands why the violence is occurring and what the point of the violence is there will not be any issues. Where problems lie are when parents buy their kids Grand Theft Auto 4 and leave him home alone with it for hours on end, who knows what he's learning or misinterpreting from a game like that?
Be involved in your kids life and expose them to everything. Don't be afraid to talk to them about violence or anything else, they're your blood after all!