This is one of those complex stories that consume Washington but frequently confuse ordinary Americans. Trump appears to be counting on that confusion to offer a fog of claims and allegations to make it appear as if Biden had done something wrong. So here’s a quick guide to Trump’s statements — and the truth.

False: Biden pushed out a Ukrainian prosecutor investigating his son

Trump has falsely claimed that Biden in 2015 pressured the Ukrainian government to fire Viktor Shokin, the top Ukrainian prosecutor, because he was investigating Ukraine’s largest private gas company, Burisma, which had added Biden’s son, Hunter, to its board in 2014.

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There are two big problems with this claim: One, Shokin was not investigating Burisma or Hunter Biden, and two, Shokin’s ouster was considered a diplomatic victory.

Biden was among the many Western officials who pressed for the removal of Shokin because he actually was not investigating the corruption endemic to the country. Indeed, he was not investigating Burisma at the time. In September 2015, then-U.S. Ambassador to Ukraine Geoffrey Pyatt publicly criticized Shokin’s office for thwarting a British money-laundering probe into Burisma’s owner, Mykola Zlochevsky.

“Shokin was not investigating. He didn’t want to investigate Burisma,” Daria Kaleniuk, of the Ukrainian Anti-Corruption Action Center, told The Washington Post in July. “And Shokin was fired not because he wanted to do that investigation, but quite to the contrary, because he failed that investigation.”

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In a 2018 appearance at the Council on Foreign Relations, Biden bragged about his role in Shokin’s removal, saying he had withheld $1 billion in loan guarantees as leverage to force action. But Biden was carrying out a policy developed at the State Department and coordinated with the European Union and the International Monetary Fund.

The Ukrainian prosecutor was regarded as a failure, and “Joe Biden’s efforts to oust Shokin were universally praised,” said Anders Aslund, a Swedish economist heavily involved in Eastern European market reforms. Getting rid of Shokin was considered the linchpin of reform efforts, but U.S. officials had a list of changes the government needed to make before it could obtain another loan guarantee.

In December 2015, Biden traveled to Kiev and decried the “cancer of corruption” in the country in a speech to the parliament. “The Office of the General Prosecutor desperately needs reform,” he noted. Shokin was removed from office three months later, and Biden announced April 15 that the loan guarantee would go forward; the agreement between the United States and Ukraine was signed June 3.

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One can certainly raise questions about Hunter Biden’s judgment in joining Burisma’s board at a time his father had a high-profile role in working with Ukraine’s government. But by continuing to claim that Biden “did” something for his son, Trump persists in spreading a false narrative about a diplomatic maneuver hailed at the time as a step toward reducing corruption in Ukraine.

False: Hunter Biden made a killing on a China deal

At various times Trump has claimed Hunter Biden “made millions of dollars from China” or “walks out of China with $1.5 billion in a fund” after hitching a ride with his father on Air Force Two. But there is no evidence to support those statements.

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In December 2013, Hunter Biden and one of his daughters flew from Japan to China with Joe Biden on Air Force Two as the vice president embarked on a diplomatic mission.

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Twelve days after he flew to Beijing, Hunter Biden joined an advisory board of a fund called BHR Partners, which had announced it would try to raise $1.5 billion. The New Yorker magazine reported that during the trip Hunter Biden arranged for his father to shake hands with Jonathan Li, who ran a Chinese private-equity fund and was one of the partners who had formed BHR.

But while Joe Biden was vice president, Hunter Biden was only on the board of the advisory firm that did not directly invest, but instead advised those who did. George Mesires, a lawyer for Hunter Biden, said he only took an equity stake in 2017, after Joe Biden was no longer vice president.

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Mesires told The Fact Checker that the investment management company “was capitalized from various sources with a total of 30 million RMB [Chinese Renminbi], or about $4.2 million, not $1.5 billion.” Because Biden acquired a 10 percent minority interest, his “capital commitment is approximately $420,000,” Mesires said.

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“To date, Mr. Biden has not received any return or compensation on account of this investment or his position on the board of directors,” Mesires added.

False: Biden lied about talking to his son

After the reports on Hunter Biden’s business deals emerged, Joe Biden told reporters: “I have never spoken to my son about his overseas business dealings.”

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Trump claimed that this was a lie because “he’s already said he spoke to his son.” But Biden had not. Instead, Trump appeared to be referring to a line in the New Yorker profile: “As Hunter recalled, his father discussed Burisma with him just once: ‘Dad said, “I hope you know what you are doing,” and I said, “I do.” ’”

That’s not much of a discussion. In any case, Biden never said he spoke to his son, as Trump claimed he did.

False: Democratic senators also threatened Ukraine’s aid

Trump claimed that three Democratic senators — Patrick J. Leahy (Vt.), Richard J. Durbin (Ill.) and Robert Menendez (N.J.) — “implied that their support for U.S. assistance to Ukraine was at stake and that if they didn’t do the right thing they wouldn’t get any assistance.” He later referred to “senators that threatened him with votes and no money coming into Ukraine if they do things.”

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Trump suggested this was the “real deal,” unlike allegations that he held up military aid to force the Ukrainian government to investigate the Bidens.

Trump is referring to a letter written in 2018, and it does not say what he claims.

The letter, written to the special prosecutor at the time, Yuriy Lutsenko, expressed concern about a New York Times report that Ukraine had stopped cooperating with special counsel Robert S. Mueller III’s investigation into Russian interference in the 2016 presidential election to avoid upsetting Trump. The letter does not threaten a loss of aid, though it notes that the Times article said that the freezing of cooperation was motivated by a worry that Trump would cut off aid. (The article was titled: “Ukraine, Seeking U.S. Missiles, Halted Cooperation with Mueller Investigation.”)

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The letter noted the signers have supported efforts to build Ukraine’s democracy and expressed “disappointment” that some lawmakers in Kiev were trying “to avoid the ire of President Trump.” The senators then ask a series of questions, seeking to clarify whether the Times report was correct and whether the Trump administration had encouraged the government not to cooperate with Mueller.

Lutsenko never responded. Since the letter was sent, the three senators have voted for nearly $870 million in additional aid to Ukraine, with Leahy and Durbin (members of the Senate Appropriations Committee) voting in committee on Sept. 26 for an additional $448 million in fiscal 2020, an increase over 2018 and 2019.

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