Ohio Gov. John Kasich said when it comes to foreign policy, “you have to know how to pick and choose.” One of Kasich’s choices would be to punch Russia in the nose.

New Jersey Gov. Chris Christie was even harsher: He said not only would he set up a no-fly zone over Syria, he would shoot down Russian warplanes that violated that zone.

Sen. Rand Paul’s response to Christie: “Well, I think if you’re in favor of World War III, you have your candidate,” he said at Tuesday night’s debate hosted by CNN.

Kasich, who advocates regime change in Syria, said he would not have toppled Iraqi dictator Saddam Hussein “if Saddam had not had weapons of mass destruction.”

He told the debate audience that Iraq needs to be broken up into three parts — Sunni, Shia, and Kurd — because the current arrangement doesn’t work.

“And for the Russians, frankly, it’s time that we punched the Russians in the nose,” Kasich said. “They’ve gotten away with too much in this world, and we need to stand up against them, not just there, but also in Eastern Europe where they threaten some of our most precious allies.”

CNN debate moderator Wolf Blitzer asked Chris Christie, “If he U.S. imposed a no-fly zone over Syria and a Russian plane encroached, invaded that no-fly zone, would you be prepared to shoot down that Russian plane and risk war with Russia?”

“Not only would I be prepared to do it, I would do it,” Christie replied. “A no-fly zone means a no-fly zone, Wolf. That’s what it means.

“See, maybe — maybe because I’m from New Jersey, I just have this kind of plain language hangup. But I would make very clear — I would not (not) talk to Vladimir Putin. In fact, I would talk to Vladimir Putin a lot. But I’d say to him, ‘Listen, Mr. President, there’s a no-fly zone in Syria; you fly in, it applies to you.’

“And yes, we would shoot down the planes of Russian pilots if in fact they were stupid enough to think that this president was the same feckless weakling that the president we have in the Oval Office is right now.”

Blitzer then turned to Rand Paul, asking him to respond to Christie.

“Well, I think if you’re in favor of World War III, you have your candidate, Paul said. “My goodness, what we want in a leader is someone with judgment, not someone who is so reckless as to stand on the stage and say, ‘Yes, I’m jumping up and down; I’m going to shoot down Russian planes.’

“Russia already flies in that airspace. It may not be something we’re in love with, the fact that they’re there, but they were invited by Iraq and by Syria to fly in that airspace.

“And so if we announce we’re going to have a no-fly zone — and others have said this. Hillary Clinton is also for it. It is a recipe for disaster. It’s a recipe for World War III.

“We need to confront Russia from a position of strength, but we don’t need to confront Russia from a point of recklessness that would lead to war,” Paul said.

For the record, Carly Fiorina said “now is not the time” to be talking with Russian President Vladimir Putin. She, like Christie, advocates a no-fly zone over Syria.

“There is a time and a place for everything. There is a time and a place for talk. And there is a time and a place for action,” Fiorina said.

“I know Vladimir Putin. He respects strength. He lied to our president’s face; didn’t bother to tell him about warplanes and troops going into Syria. We need to speak to him from a position of strength.

“So as commander in chief, I will not speak to him until we’ve set up that no-fly zone; until we’ve gathered our Sunni-Arab allies and begun to deny ISIS territory; until I’ve called the supreme leader of Iran and told him new deal — new deal. We, the United States of America, are going to cut off the money flow, which we can do; which we don’t need anyone’s permission or collaboration to do.

“And I will not speak to him personally until we’ve rebuilt the 6th Fleet a little bit right under his nose; rebuilt the missile defense program in Poland right under his nose; and conducted a few military exercises in the Baltic states.”