demonstrate against someone or something
to make a public show against someone or something. The citizens demonstrated against the new policies. A number of protestors demonstrated against the mayor.
demonstrate for someone or something
to make a public show in favor of someone or something. We will all demonstrate for Walter's candidacy. A number of supporters demonstrated for the mayor.
demonstrate something to someone
to show someone how something works. Would you please demonstrate this DVD player to me? I may want to buy it. The new products were demonstrated to the board of directors in advance.