WASHINGTON — You’d think from the latest Republican presidential debate that Donald Trump and Carly Fiorina have special insights into what makes Russian Vladimir Putin tick because the candidates have been up close and personal with the Kremlin’s man himself.

Not so much.

Trump declared himself a “stablemate” with Putin because both were on the same TV program — once, and in different segments, thousands of miles apart. Fiorina claimed a “private meeting” with Putin, but the setting was a holding room where they sat before giving speeches; not exactly a summit.

The Putin puffery proved to be one of the odder episodes of an evening that brought viewers a variety of flubs and exaggerations.

Some of the claims Tuesday night and how they compare with the facts:

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TRUMP: Speaking of Putin, “I got to know him very well because we were both on ’60 Minutes,’ we were stablemates, and we did very well that night. But, you know that.”

FIORINA: Saying the U.S. is currently in a weak position with Russia and that is “one of the reasons I’ve said that I would not be talking to Vladimir Putin right now, although I have met him as well, not in a green room for a show, but in a private meeting.”

THE FACTS: Trump and Fiorina seemed to be contesting who knows Putin better — Fiorina from a chance meeting in a holding room before she and Putin addressed a Beijing conference in 2001, or Trump from having appeared on the same “60 Minutes” program as Putin in September.

At least Fiorina actually met Putin. During a September appearance on “The Tonight Show,” she described how they sat in adjacent chairs for 45 minutes while they each waited to speak. Trump’s only connection to the Russian leader was that they both appeared on the same show. He was interviewed in New York, Putin in Moscow, and they weren’t even in the same segment on the program.

BEN CARSON: “Every time we raise the minimum wage, the number of jobless people increases.”

THE FACTS: Actually, that usually doesn’t happen. When the minimum wage was increased in 1996 and 1997, the unemployment rate fell afterward. In June 2007, when the first of three annual minimum wage increases was implemented, the unemployment rate was unchanged until the Great Recession began six months later.

Economic research has found that when states raise their minimum wages higher than neighboring states, they don’t typically fare any worse than their neighbors.

It’s not known, though, what would happen to jobs if the minimum wage were doubled to $15. That’s something many fast-food workers who demonstrated before the debate were demanding.

MARCO RUBIO: “Welders make more money than philosophers.”

Not so, on average.

Rubio is arguing that the U.S. has failed to invest in vocational training — a point also stressed by President Barack Obama’s now-defunct jobs council. But Rubio is wrong to suggest that studying philosophy is a waste of money and time.

PayScale, a firm that analyzes compensation, put the median midcareer income for philosophy majors at $81,200 in 2008, with welders making $26,002 to $63,698.

Georgetown University’s Center on Education and the Workforce said in a 2014 analysis that median incomes were $68,000 for people with an advanced degree in philosophy or religious studies.

So knowing Plato and getting a college degree still pays off.

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TED CRUZ, holding out his hand and unfolding one finger at a time to punctuate his point: “Five major agencies that I would eliminate: the IRS (his thumb), the Department of Commerce (index finger), the Department of Energy (middle finger), uh, the Department of Commerce (ring finger), and HUD (pinkie).”

THE FACTS: He flubbed his own list, naming the Commerce Department twice and leaving out one of the agencies he proposes to close, according to his website: the Education Department.

Rick Perry, then Texas governor, had almost precisely the same problem at a GOP primary debate in November 2011, coming up with the names of only two of the three departments he wanted to close, Commerce and Education. “Oops,” he said after failing to name the third agency, Energy, a slip that haunted him for the rest of his campaign.

But Cruz moved on without anyone calling him on the gaffe.

CRUZ: Since 2008, the economy has grown on average only 1.2 percent a year, showing “the Obama economy is a disaster.”

THE FACTS: That average is correct as far as it goes, but it masks the fact that Obama inherited a raging recession in his first year, when the economy shrank by 2.5 percent. In the five years since, the economy expanded an average of 2 percent, more than Cruz’s figure but still a relatively weak recovery in historical terms.

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JEB BUSH: “We could get to 4 percent growth.”

THE FACTS: That’s a highly improbable target because of forces in the economy that are beyond the control of any president.

Those forces have been decades in the making: an exodus from the workforce of the huge generation of baby boomers, rising automation and low-wage competition overseas. Those factors and more have limited income growth, which in turn cuts into the consumer spending that drives most economic growth.

Bush frequently holds out hope of 4 percent growth, but even conservative economists who like his fiscal and tax plans consider it a false hope. According to current forecasts, growth is expected to average roughly half that rate.

TRUMP: The Pacific trade agreement signed by Obama with 11 other nations “was designed for China to come in through the back door and take advantage of everyone. … China takes advantage (of the U.S.) through currency manipulation.”

THE FACTS: The Trans-Pacific Partnership trade pact, signed last month, does not include China and is intended to give the United States more influence in Asia as a counterweight to China’s rising economic power. Obama argues that China could join later, but without having any influence on the agreement’s terms.

Regarding currency manipulation, Trump is recycling an outdated claim. He has argued that China keeps its currency undervalued by 15 percent to 40 percent, which would make its exports cheaper and more attractive overseas. Yet the Peterson Institute for International Economics, which had criticized China for keeping its currency artificially low, concluded in 2012 that China’s currency by then was fully valued. The International Monetary Fund has reached the same conclusion.

FIORINA: “Obamacare isn’t really helping anyone.”

THE FACTS: Public opinion remains divided over Obama’s health care law, but it’s clearly helping many people.

In the two years since the law’s coverage expansion began, the share of Americans without health insurance has declined to 9 percent, a historic low. That translates to roughly 16 million people gaining coverage, even as the economy and hiring have been improving.

Also as a result of “Obamacare,” people with pre-existing health conditions can no longer be turned away by insurers, and everyone is required to have coverage or face fines.

While the coverage mandate in Obama’s law remains highly unpopular, state-run high-risk health insurance pools like the one Fiorina proposes to replace the law have been tried before by many states and failed to solve the coverage problem. The main reason was cost. The risk pools grouped people who couldn’t get private insurance because of health problems, resulting in very high premiums and pricing out low-income people. Some risk pools had long waiting lists.

As a rule, broad insurance pools that include lots of healthy people seem to be better for covering people with health problems than programs specifically targeted to that group.

TRUMP: People who are in the U.S. illegally are “going to have to go out and hopefully they get back. But we have no choice if we’re going to run our country properly.”

JOHN KASICH: “If people think that we are going to ship 11 million people who are law-abiding, who are in this country, and somehow pick them up at their house and ship them out of Mexico — to Mexico, think about the families. Think about the children.”

TRUMP: President Dwight Eisenhower “moved 1.5 million illegal immigrants out of this country. … We have no choice.”

THE FACTS: Eisenhower did oversee a deportation program in 1954, but it involved nowhere near the 11 million people now estimated to be in the U.S. illegally and it was criticized for violating the civil rights of deportees. At the time, the government claimed to have removed about 1.3 million immigrants, though historians now say that figure was inflated. The deportation program focused on Arizona, California and later Texas, targeting farm and industrial workers.

Another repatriation, in the 1930s, had seen the return of 500,000 to 1 million Mexican immigrants and Mexican-Americans, also drawing civil rights complaints and in some cases expelling U.S. citizens along with their immigrant relatives.

Any similar effort today would likely face court challenges, adding to a 456,000-case backlog that already means it can take years for an immigrant’s deportation case to be heard by a judge.

Associated Press writers Ricardo Alonso-Zaldivar, Paul Wiseman, Alicia Caldwell, Jill Colvin and Ken Dilanian contributed to this report.

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