Card Rulings talk:Magic Jammer

If you use a card like magic jammer or hand destruction. Do you HAVE to discard the cards for it to work? It doesn't say discard cards TO draw 2 cards for hand destruction's effect. And it doesn't say discard 1 card TO negate the effect of one spell card. It just says DISCARD and if you have 0 cards to discard, can you still activate these cards?