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As voters in South Carolina took to the polls on Saturday, Nikki Haley has vowed to continue challenging former President Donald Trump for the Republican nomination — to the dismay of her onetime boss.

In recent weeks, Trump and Haley, former governor of South Carolina and U.N. ambassador in the Trump administration, have dialed up their attacks on each other.

Trump has mocked the absence of Haley's husband, Maj. Michael Haley, a National Guards member who is deployed to Africa. His campaign suggested that her staying in the race, despite being well behind Trump in delegates, was "like any wailing loser hellbent on an alternative reality." Haley has said that her rival has "gotten more unstable and unhinged" and that he has "mental deficiencies."

But while attacking each other's record and policies, both have turned to false and misleading claims.

Here's a fact check.

What was said

"Every poll shows that he can't beat Biden. Some are down by 5, some are down by 7. On his best day, it's margin of error." — Haley, referring to Trump during a Fox News town hall this month.

False. National general election polls do show a tight race in a potential Trump-Biden rematch, and Haley has emphasized select polls that show her beating Biden by double digits. But Trump comes in slightly higher than his successor in many — though not all — surveys.

For example, Morning Consult recently found Trump leading Biden by 4 points, outside the survey's margin of error.

Other polls show Trump leading Biden, albeit within the margin of error: an NBC News poll in January surveying registered voters found that 47% said they would vote for Trump, compared with Biden's 42%. (However, the results shifted in Biden's favor when the respondents were asked to consider the same matchup if Trump were to be convicted of a felony.) In yet other polls, Biden holds a slight lead over Trump.

As of Friday, the Real Clear Politics average, which incorporates multiple polls, showed Trump ahead of Biden by 1.9 percentage points. The average in a hypothetical Haley-Biden matchup showed Haley ahead by 4.9 percentage points.

"The polls at this point aren't very useful for predicting the eventual winner, but they do indicate that it's likely to be a close election," Alan Abramowitz, a political scientist at Emory University, said of a Trump-Biden contest.

What was said

"Nikki Haley wants to charge the working class a 23% national sales tax." — Trump during a January rally.

This is misleading. Haley has not called for such a policy as she campaigns for president. Instead, Trump's campaign has cited a 2012 post from Haley supporting a "Fair Tax."

"Yes, I support the Fair Tax and any reform that would eliminate income tax," Haley wrote in the 2012 post on Facebook.

Haley's campaign did not say what she was referring to in that post, but she could have been referencing the Fair Tax Act, a proposal that has been repeatedly put forward in Congress to no avail. The legislation seeks to eliminate federal taxes — including income, payroll, estate and gift taxes — and instead impose a national sales tax of 23%. It also calls for abolishing the Internal Revenue Service.

Many prominent Republicans, including Ron DeSantis, now governor of Florida, and former Vice President Mike Pence, have supported the proposal at some point over the years. Critics of the legislation have said the bill would raise the tax burden of many Americans but spare the wealthy.

However, Haley also could have been referring to state-level "fair tax" legislation that lawmakers in South Carolina — and elsewhere — were proposing around that time, calling for the elimination of specific state taxes, including the income tax, in favor of a higher state sales tax. (South Carolina's proposal would have reportedly raised the sales tax to an estimated 6% to 7% from 5%.) In a 2015 Facebook comment, Haley clearly indicated she supported the state proposal, saying that "the legislature knows that if they send it to me, I will sign it."

What was said

"Donald Trump needs to answer to the fact that why did he propose an 18-cent per gallon gas tax increase in 2018 when he was president?" — Haley this month during a Fox News town hall.

False. Trump never formally proposed a gas tax increase, as Haley suggested. Instead, some lawmakers said that Trump had entertained the idea of increasing the gas tax by 25 cents — not 18 cents — during a private, bipartisan meeting.

After that meeting in February 2018, Sen. Thomas Carper, a Democrat, said Trump had endorsed the idea to pay for an infrastructure plan released by the White House. Some critics quickly denounced the notion.

It was not the first time Trump had signaled openness to a gas tax hike. In 2017, he told Bloomberg News that he would consider such an increase. And in January 2018, The Washington Post, citing an unidentified person familiar with the deliberations, reported that Trump had privately "mused about a gas tax increase to 50 cents per gallon."

Nevertheless, Trump never formally put forward such proposals.

The Trump campaign has also repurposed a misleading claim about Haley's record on gas taxes. A recent ad suggests Haley called for raising the gas tax in South Carolina as governor but has since lied about it. In fact, Haley rebuffed calls to increase the state gas tax as a stand-alone measure and proposed raising it by 10 cents over three years only if the state reduced the income tax rate to 5%, from 7%, and made changes to the state's Transportation Department.

What was said

Nikki Haley "actually dropped Romney for a little while for Obama." — Trump during a rally this month.

False. There is no record of Haley politically backing former President Barack Obama. The Trump campaign did not respond to requests for evidence of such support.

Trump similarly claimed on Truth Social that Haley "was also a Barack Hussein Obama supporter as seen here." The post included a video clip from a 2012 campaign event for Mitt Romney, then a Republican presidential candidate, showing Haley accidentally using Obama's name when she meant to reference Romney.

Haley said: "Obama wants to strengthen our military and will never apologize for America." But Romney quickly corrected her, as the clip shows, and the two laughed as Haley recognized the slip.

What was said

"What is Trump saying he'll actually do in office? A 10% across-the-board tax increase." — Haley campaign in an ad this month.

This is misleading. Trump hasn't proposed a "10% across-the-board tax increase" on Americans, but he did float a proposal to impose a 10% tariff on imported goods — which economists say would affect prices for U.S. companies and consumers.

The ad cites a January CNBC article about comments Trump made in an August interview with Fox Business.

"I think when companies come in and they dump their products in the United States, they should pay automatically, let's say, a 10% tax," Trump told Larry Kudlow, who served as director of the National Economic Council during the Trump administration. "That money would be used to pay off debt."

"A 10 percent tariff on all imports is a 10 percent across-the-board tax on imports," Katheryn Russ, an economics professor at the University of California, Davis, said in an email. "It is not an across-the-board tax on all goods."

There are elements of Trump's vision that remain unclear, including whether the new tariff would apply to imports from countries with which the United States has free trade deals, as The New York Times has reported.

Experts have said Trump's proposal would result in higher prices for Americans and most likely cause trading partners to retaliate. An economist at the right-leaning Tax Foundation said such a 10% tariff would effectively "raise taxes on American consumers by more than $300 billion a year" and slightly reduce the size of the U.S. economy.

Tariffs are paid by the U.S.-based importer. While exporters could absorb some of the cost by lowering prices, research on tariffs put in place under the Trump administration suggests the costs largely fell on U.S. firms and consumers.

How much of a new tariff would get shouldered by consumers remains an open question, Russ said, noting that importing firms could reduce profit margins instead of passing the cost to consumers. But tariffs can also result in higher prices for domestic products — if a firm raises prices strategically, given more expensive imported products on the market, or if the manufacturer relies on imported inputs.

Imported goods and services were equivalent to about 14% of the United States gross domestic product last year, according to federal data.

What was said

"Nikki Haley joined Biden in opposing President Trump's border wall." — Trump campaign in an ad this month.

False. Haley did not oppose Trump's border wall. She said in 2015, when Trump launched his first bid for the presidency, that a wall was not the sole answer.

To support its claim about the border wall, the ad cites a 2023 Time article. But that article doesn't offer evidence that Haley opposed the wall. Instead, it quotes comments Ms. Haley made during a National Press Club event, linking to a Washington Post opinion piece from September 2015 describing the event.

The Time article quoted Haley telling Republicans "to remember that the fabric of America came from these legal immigrants," and drawing a distinction between them and immigrants who enter the country illegally.

Ms. Haley's full comments made clear that she did not reject the idea of a border wall, as long as it was part of a broader plan.

"Don't say you're just going to build a wall, because a wall's not going to do it," she said at the time. "You've got to have commitment of ground troops, equipment, money — all of that, to bring it together."

During her campaign for president, Haley has also supported the idea of expanding the wall.

This article originally appeared in The New York Times.