WASHINGTON (AP) — Herman Cain's 9-9-9 tax plan ignited plenty of sparks in the Republican presidential debate Tuesday night, as did testy exchanges between Mitt Romney and Rick Perry. In those instances and more, the facts took a bit of a beating.

A look at the accuracy of some of the claims in the Las Vegas debate:

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HERMAN CAIN: "It does not raise taxes on those that are making the least."

THE FACTS: An independent analysis of his tax plan, released Tuesday, concluded otherwise. The Tax Policy Center, a Washington think tank, said Cain's plan would increase taxes on 84 percent of U.S. households, hitting low- and medium-income households the hardest. The analysis said that households making $10,000 to $20,000 would see whopping tax increases averaging $2,705 — an increase of nearly 950 percent.

The rich, however, would get big tax cuts, the analysis said.

Cain's plan would scrap current taxes on income, payroll, capital gains and corporate profits. He would replace them with a 9 percent tax on income, a 9 percent business tax and a 9 percent national sales tax.

The study is in line with economic theorists — whether on the left or right — who note that sales taxes tend to hit low-income families the hardest because they spend more of their income than wealthier families do.

Unlike most states, Cain's plan would not exempt food or medicine from sales taxes. Used items, however, would be exempt.

Cain said his plan would create zones where people and businesses could get additional tax deductions, which would reduce taxes for low-income people. The Tax Policy Center said it did not take the zones into account because the Cain campaign did not provide any details on how they would work.

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RICK PERRY: "Mitt, you lose all of your standing, from my perspective, because you hired illegals in your home and you knew about it for a year. And the idea that you stand here before us and talk about that you're strong on immigration is on its face the height of hypocrisy."

MITT ROMNEY: "I don't think I've ever hired an illegal in my life."

THE FACTS: The truth is that Romney, former Massachusetts governor, never directly hired an illegal immigrant. But he hired a landscaping company that employed them.

In bringing up the matter, Texas Gov. Perry resurrected a charge that has dogged Romney since his last presidential bid. In 2006, Romney learned that the landscaper of his suburban Boston home had employed illegal immigrants. He gave the company a second chance under the condition that it would no longer employ undocumented workers.

But in 2007, during the height of his first Republican presidential campaign, the same company was caught employing illegal immigrants at Romney's home. Romney then fired the landscaper.

At the time, and again Tuesday night, Romney said there's only so much an individual can do when hiring a legitimate company.

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ROMNEY to PERRY: "You were the chairman of Al Gore's campaign."

THE FACTS: Romney's claim was misleading, at best. He neglected to mention that Perry's role in Gore's failed 1988 campaign for the Democratic presidential nomination was limited to Texas. It was also marginal.

Perry was a Democrat serving in the state legislature at the time and had no significant leadership role in Gore's third-place finish in Texas. He was one of 28 Democratic Texas lawmakers who endorsed Gore. In any event, he was far from being "the chairman" of Gore's campaign. Perry switched parties in 1989 and successfully ran for state agriculture commissioner as a Republican.

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RICK SANTORUM: "(Perry) sent a letter the day of the vote on the floor of the House saying, pass the economic plan. There was only one plan, and that was the plan that was voted on the floor. It was TARP."

PERRY: "I'm just telling you I know what we sent, I know what the intention was. You can read it any way you want, but the fact of the matter, I wasn't for TARP, and have talked about it for years since then."

THE FACTS: In October 2008, Perry appeared to be both for and against the Troubled Asset Relief Program in the same week.

As chairman of the Republican Governors Association, he co-wrote a letter to Congress with his Democratic counterpart that is hard to interpret as anything other than a call to pass the bailout that became known as TARP.

"We strongly urge Congress to leave partisanship at the door and pass an economic recovery package," said the letter. It was dated Oct. 1, just after the House rejected an initial version of the economic recovery bill. That vote triggered an 800-point drop in the Dow Jones industrial average.

But the next day, Perry was quoted in The Dallas Morning News as saying that while he favored some kind of economic recovery plan to help taxpayers, "in a free-market economy, government should not be in the business of using taxpayer dollars to bail out corporate America."

Within days, a new version of the bailout was passed by the Senate, then the House, and signed into law by Republican President George W. Bush.

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MICHELE BACHMANN: "Even the Obama administration chose to reject part of Obamacare. ... Now the administration is arguing with itself."

THE FACTS: True, the administration is moving to scrap a long-term insurance program that was part of Obama's health care law. But it would be wrong to take that as a sign the administration is losing faith in the overhaul. Quite the contrary.

Unlike the central provisions of the health care law, the long-term insurance plan, called CLASS, was voluntary. From an accounting viewpoint, that was its fatal weakness.

Without some reason for large numbers of healthy people to sign up, experts warned all along that CLASS would attract too many people in frail health. Rising benefit costs would send premiums spiraling upward. Healthier people would drop out, and eventually taxpayers would have to bail CLASS out.

Obama's health insurance mandate, requiring nearly everyone to have insurance, protects his overhaul from a similar fate.

"You have to have a broad risk pool," said Robert Bixby, executive director of the Concord Coalition, a nonpartisan group that advocates cutting the federal deficit. "By mandating coverage, (the health care law) creates a broad risk pool and that makes the system much more sustainable."

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ROMNEY to PERRY: "You probably also ought to tell people that if you look over the last several years, 40 percent, almost half the jobs created in Texas were created for illegal aliens, illegal immigrants."

THE FACTS: There's some basis for the assertion that significant numbers of jobs were taken by immigrants, but it's a stretch to try to pinpoint how many of them may have been in the country illegally.

A September report from the conservative-leaning Center for Immigration Studies concluded that 81 percent of new Texas jobs were taken by newly arrived immigrants, basing that on a government survey used to calculate the unemployment rate. The group also estimated that about half of those jobs were taken by illegal immigrants.

The government survey that is the source of the numbers asks people whether they are foreign or native born, but doesn't ask about their legal status. The center's estimate was an extrapolation based on other government estimates of illegal immigrant populations.

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BACHMANN: "The biggest problem with this administration and foreign policy is that President Obama is the first president since Israel declared her sovereignty (to) put daylight between the United States and Israel."

THE FACTS: Israel and the U.S. have had their disagreements and have showed them — often in far starker contrast than today. And the consequences have been far greater, too.

While the Obama administration has criticized Israeli settlement construction on disputed lands, President George H.W. Bush actually punished the Jewish state for the policy by docking housing loan guarantees. President Jimmy Carter experienced tensions with the Israeli government over his public support for a Palestinian homeland, and President Ronald Reagan harshly criticized Israel for a military attack on an Iraqi nuclear plant in the 1980s.

Even in times of war, the U.S. and Israel have differed publicly. The worst disagreement came in 1956 when the United States demanded that Israel, Britain and France end their joint war against Egypt.