WASHINGTON (AP) — President Donald Trump has a sophisticated machine at his disposal for gathering and analyzing information: the U.S. government.

But many of his inflammatory statements come from another place, an ethereal world where his sources are never identified:

“They say. ... Well, that’s what the word is. ... That’s the way it was explained.”

Over the past week of impeachment hearings, Trump blew past the consensus of national security and foreign policy professionals, dismissing them as Never Trumpers , and dug in with his theory of Ukrainian misdeeds that they said is false.

In the course of that, he continued to describe an American company as a Ukrainian one and its American chief as a Ukrainian rich man.

Here’s a look at some of the rhetoric from and about the House Intelligence Committee hearings as well as some remarks by Democratic presidential contenders who tried in their latest debate to be heard above the impeachment din:

UKRAINE

TRUMP, referring to Democrats: “The FBI went in and they told them, get out of here, you’re not getting — we’re not giving it to you. They gave the server to CrowdStrike, or whatever it’s called, which is a country — which is a company owned by a very wealthy Ukrainian. And I still want to see that server. You know, the FBI has never gotten that server. That’s a big part of this whole thing. Why did they give it to a Ukrainian company? Why?” — Fox News interview Friday.

THE FACTS: Trump’s statement is false in multiple ways.

CrowdStrike is not a Ukrainian company — it is based in Sunnyvale, California. It is not owned by a Ukrainian, but rather an American who emigrated to the U.S. as a child — from Russia, not Ukraine.

The cybersecurity firm made the original determination that Russia was responsible for the 2016 hack of Democratic emails that were subsequently disclosed by WikiLeaks. The company counts among its clients the National Republican Congressional Committee, for which it investigated email thefts by unidentified hackers during the 2018 campaign.

When Trump says the “FBI has never gotten that server,” he is referring to the fact that the FBI did not receive physical servers from the Democratic National Committee after its emails were hacked in the 2016 campaign.

Instead, the FBI relied on detailed forensics provided by CrowdStrike. The FBI confirmed those findings. Using that evidence, special counsel Robert Mueller’s team charged 12 Russian military intelligence officers with the hack.

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Still, Trump persists not only in misidentifying the nationality of the owner and what country the firm is from, but in advancing the notion that Ukrainians hacked the DNC and made it look as if Russians did it.

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TRUMP: “A lot of it had to do, they say, with Ukraine. ... They have the server, right, from the DNC, Democratic National Committee, you know. ... Well, that’s what the word is. ... That’s the way it was explained.” — Fox News interview Friday.

THE FACTS: Trump is shrugging off not only the week’s testimony of current and former aides at the hearing, but advice going back months from officials who told him such assertions are invalid.

None of the witnesses who testified at the hearings — including those the Republicans wanted to hear from — gave credence to Trump’s theory that Ukraine attacked the U.S. election and tried to make Russia look like the villain.

Several testified to the contrary, that there is no evidence of Ukraine interference.

Even before his July phone call pressing Ukraine’s president to investigate the theory, his own staff repeatedly told him it was “completely debunked,” Trump’s first homeland security adviser, Tom Bossert, said in September.

“Fictions,” a former senior director on the National Security Council for Russia and Europe, Fiona Hill , testified Thursday.

She told committee members: “I would ask that you please not promote politically driven falsehoods that so clearly advance Russian interests.”

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GORDON SONDLAND

TRUMP: “I don’t know him very well. I have not spoken to him much. This is not a man I know well. He seems like a nice guy, though. But I don’t know him well.” — remarks to reporters Wednesday.

THE FACTS: That’s not credible. Testimony by several officials revealed that Sondland, Trump’s EU ambassador, was in frequent contact with Trump around the time Trump spoke with Ukrainian President Volodymyr Zelenskiy about doing a politically beneficial “favor.”

Tim Morrison , the former NSC Russia and Europe senior director, who took over from Hill in July, told House investigators that Sondland and Trump had spoken approximately five times between July 15 and Sept. 11 — the weeks that $391 million in U.S. assistance was withheld from Ukraine before it was released as Trump pressed for the favor. Morrison said the ambassador “related to me he was acting — he was discussing these matters with the president.”

Sondland himself changed his testimony Wednesday to acknowledge more contacts with Trump than previously revealed.

As recently as Oct. 8, Trump had tweeted that Sondland was a “really good man and great American.”

Sondland donated $1 million to Trump’s inaugural committee before being named the U.S. ambassador to the European Union.

But Trump quickly became less familiar with his ambassador when Sondland testified that the president wanted a Ukrainian investigation of Democrats as a condition for his releasing U.S. military aid to that country.

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PAM BONDI, White House adviser: “We’re going to hear what Gordon Sondland has to say today. He was the ambassador to the Ukraine.” — remarks to reporters Wednesday.

THE FACTS: Sondland is the U.S. ambassador to the European Union, not Ukraine.

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APPLE MANUFACTURING

TRUMP: “Today I opened a major Apple Manufacturing plant in Texas that will bring high paying jobs back to America. Today Nancy Pelosi closed Congress because she doesn’t care about American Workers!” — tweet Wednesday.

THE FACTS: Neither happened.

Trump visited a factory in Austin, Texas, that has made the Mac Pro for Apple since 2013.

Apple announced in September that it would continue having the Mac Pro line made in Austin, after the Trump administration agreed to waive tariffs on certain computer parts from China. It also plans to expand its already deeply rooted business in Austin and said Wednesday it has started construction of its new campus in the city.

None of that equates to Trump’s false claim to have opened an Apple plant Wednesday.

Meantime, the House worked into Wednesday evening, after Trump’s false tweet that Pelosi had shut Congress, and again Thursday before breaking for Thanksgiving week.

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IMPEACHMENT HEARING

REP. ADAM SCHIFF, Democratic committee chairman: “I think the American people can be forgiven if they have the same impression, listening to some of the statements of my colleagues during this hearing, that Russia didn’t intervene in our election. It was all the Ukrainians.” — hearing Thursday.

HILL: “Based on questions and statements I have heard, some of you on this committee appear to believe that Russia and its security services did not conduct a campaign against our country and that perhaps somehow for some reason Ukraine did. This is a fictional narrative that is being perpetrated and propagated by the Russian security services themselves.” — hearing Thursday.

REP. ELISE STEFANIK, Republican of New York: “Not a single Republican member of this committee has said that Russia did not meddle in the 2016 elections. ... To have our Democratic colleagues say these untruthful statements just reeks of political desperation.” — hearing Thursday.

THE FACTS: Stefanik may be right that Republicans on the committee did not explicitly deny that Russia attacked the U.S. election. Yet Schiff and Hill may also be right in saying that Republicans left that impression at the hearings.

Some Republicans on the committee repeatedly gave credence to the conspiracy theory that holds that Ukrainians actually hacked the Democratic National Committee emails, perhaps with a server that was in their country, and made it look as if Russia did it. To buy into this theory is to discount Russian culpability.

A 2018 report by the then-Republican majority of the House Intelligence Committee agreed with U.S. intelligence agencies that Russia interfered in the election, but disagreed with parts of the agencies’ assessment that said Russia did so to help Trump.

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REP. DEVIN NUNES of California: Trump has good reason to be wary “of widespread corruption in that country.” — hearing Thursday.

THE FACTS: The committee’s top Republican is pointing to an oft-made defense by Trump and GOP allies that he withheld military aid to Ukraine because of concerns about corruption. But the hearings produced bountiful testimony that Trump was singularly focused on making Democrats the target of Ukrainian investigations.

In his first phone call with Ukraine’s new leader, in April, the White House said at the time that Trump discussed his interest in having Ukraine rein in widespread corruption. But in the recently released rough transcript of the call, he did not mention corruption at all.

Trump had $391 million in congressionally approved U.S. assistance withheld from Ukraine from July to September.

The Defense Department had already certified to congressional committees on May 23 that Ukraine had made enough progress on reducing corruption to receive the military assistance. Before the July hold on the aid, the Trump administration had approved sending aid to Ukraine nearly 50 times without holding it because of corruption concerns.

Witnesses testified that Trump did not articulate concerns about Ukraine corruption other than expressing interest into investigations that would benefit him politically.

In his July 25 call, Trump told Zelenskiy as they discussed military aid, “I would like for you to do us a favor, though” and investigate Joe Biden, his son and Democrats going back to the 2016 U.S. election, citing in part the discredited conspiracy theory involving Ukraine in that election.

Trump ultimately released the aid, on Sept. 11, after Congress became aware of what he had done. A few days earlier, congressional committees had begun looking into the matter, aware that a whistleblower had a complaint in motion.

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NUNES: “Now that the whistleblower has successfully kickstarted impeachment, he has disappeared from the story, as if the Democrats put the whistleblower in their own witness protection program.” — hearing Tuesday.

THE FACTS: The whistleblower hasn’t “disappeared.” That person has offered to submit written testimony; Republicans have rejected that.

Trump and his GOP allies are suggesting that the whistleblower’s complaint is false, and so the person has vanished. But key details were corroborated by people with firsthand knowledge of the events who appeared on Capitol Hill.

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TRUMP: “Right now you have a kangaroo court headed by little shifty Schiff, where we don’t have lawyers, we don’t have witnesses, we don’t have anything.” — Cabinet meeting.

THE FACTS: Depends on the meaning of “we.” Republicans on the committee had a lawyer asking questions of the witnesses, so it’s not true that they had no legal representation. And several witnesses were invited at the request of Republicans on the committee.

It’s also true, though, that Trump himself did not have a lawyer speaking for him at the hearings. That’s not unusual. The inquiry is meant to be a fact-finding process and the president is not charged with anything.

He will have legal representation if the House Judiciary Committee moves ahead to draft articles of impeachment against him.

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DEMOCRATIC DEBATE

BERNIE SANDERS: “What the scientists are telling us is if we don’t get our act together within the next eight or nine years, we’re talking about cities all over the world, major cities going underwater, we’re talking about increased drought, we’re talking about increased extreme weather disturbances.” — Democratic debate Wednesday.

THE FACTS: To be clear, the world’s big cities aren’t going to go underwater for good in as soon as eight to nine years. The Vermont senator’s reference to eight to nine years seems to refer to standard warnings of the expected temperature increases kicking in by roughly 2030, and the progressively worse weather extremes that will keep following.

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JOE BIDEN: “The fact is the vast majority of Democrats do not support Medicare for All.” — Democratic debate.

THE FACTS: That statement is at odds with a Kaiser Family Foundation poll out this week. It found that 77% of Democrats support Medicare for All.

Even more — 88% — support a “public option” proposal such as the one Biden advocates. It would allow people to buy into a new government insurance plan modeled on Medicare, but it would not completely replace private insurance. Overall, 53% of Americans support Medicare for All, while 43% oppose it, according to the Kaiser poll.

It’s also true, though, that public support for Medicare for All declines when costs and other, similar details are introduced in the polling.

ELIZABETH WARREN: “Today in America — a new study came out — 20 years out, (of) whites who borrowed money, 94% have paid off their student loan debt, 5% of African Americans have paid it off.” — Democratic debate.

THE FACTS: That’s not right. Warren appears to be citing a September report from Brandeis University’s Institute on Assets and Social Policy. The study found that, 20 years after starting college, 49% of white borrowers had paid off their loans entirely (not 94% of them) compared with 26% of black borrowers (not 5%).

The study also found that the typical white student had paid off 94% of his or her debt, while the typical black borrower had only paid off 5%. Warren cited those statistics, but in the wrong way.

She’s correct that there are disparities by race when it comes to paying back student loans. Other studies have similarly found that black borrowers are at greater risk of default than their white counterparts.

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TULSI GABBARD: “The most recent example of inexperience in national security and foreign policy came from your recent careless statement about how you as president would be willing to send our troops to Mexico to fight the cartels.” — Democratic debate.

PETE BUTTIGIEG: “That is outlandish, even by the standards of today’s politics. ... I was talking about U.S.-Mexico cooperation. We’ve been doing security cooperation with Mexico for years, with law enforcement cooperation and a military relationship that could continue to be developed with training relationships, for example. Do you seriously think anybody on this stage is proposing invading Mexico?” — Democratic debate.

GABBARD: “You were asked directly whether you would send our troops to Mexico to fight cartels and your answer was yes. The fact checkers can check this out.” — Democratic debate.

THE FACTS: Neither offered a fully accurate account in their exchange.

Gabbard did not accuse Buttigieg of being open to “invading” Mexico, as he suggested she did. But she did not explain the context of his remarks at a Latino-issues forum in Los Angeles last Sunday.

At the forum, he heavily conditioned the idea of sending troops to help Mexico fight the drug and gang war, saying he would only do so if Mexico wanted the assistance as part of a security partnership.

“There is a scenario where we could have security cooperation as we do with countries around the world,” he said in Los Angeles. “I would only order American troops into conflict if there were no other choice, if American lives were on the line and if this were necessary in order for us to uphold our treaty obligations.

“But we could absolutely be in some kind of partnership role if and only if it is welcome by our partner south of the border.”

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Associated Press writers Eric Tucker, Mary Clare Jalonick, Lisa Mascaro, Lynn Berry, Mark Sherman, Kevin Freking, Ellen Knickmeyer and Ricardo Alonso-Zaldivar in Washington, Collin Binkley in Boston, Kathleen Ronayne in Los Angeles and Amanda Seitz in Chicago contributed to this report.

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