WASHINGTON — President Donald Trump cast a fog of misinformation over the U.S. trade dispute with China, floating inaccurate numbers and skewed economic theories as big tariffs kicked in on Chinese goods.

At stake in the rupture is a trading relationship between the world’s two largest economies that employs nearly 1 million Americans, supplies affordable goods to U.S. households and, in the view of Trump and a bipartisan group of trade hard-liners, puts U.S. business at an unfair disadvantage.

Trump’s torrent of tweets on the subject Friday followed a rally infused with familiar falsehoods about his achievements (the economy, veterans’ health) and grievances (the Russia inquiry). A look at his words over the past week:

TRADE

TRUMP: “Tariffs are NOW being paid to the United States by China of 25% on 250 Billion Dollars worth of goods & products. These massive payments go directly to the Treasury of the U.S.” — tweet Friday.

THE FACTS: This is not how tariffs work. China is not writing a check to the U.S. Treasury. The tariffs are paid by American companies, which usually pass the cost on to consumers through higher prices. One of the theories is that the higher prices will encourage consumers to buy goods made in the U.S. or elsewhere instead. But the risk is that consumers could simply respond by spending less than they otherwise would, which would hurt growth.

The burden of Trump’s tariffs on imports from China and other countries falls entirely on U.S. consumers and businesses that buy imports, said a study in March by economists from the Federal Reserve Bank of New York, Columbia University and Princeton University. By the end of last year, the study found, the public and U.S. companies were paying $3 billion a month in higher taxes and absorbing $1.4 billion a month in lost efficiency.

A coalition of U.S. trade organizations representing retail businesses, tech, manufacturing and agriculture said this past week: “For 10 months, Americans have been paying the full cost of the trade war, not China.” It said: “To be clear, tariffs are taxes that Americans pay, and this sudden increase with little notice will only punish U.S farmers, businesses and consumers.”

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TRUMP: “Your all time favorite President got tired of waiting for China to help out and start buying from our FARMERS, the greatest anywhere in the World!” — tweet Friday.

THE FACTS: The notion that China doesn’t buy from U.S. farmers is false. China is the fourth-largest export market for U.S. agriculture. It bought $9.3 billion in U.S. agricultural products last year.

As for calling himself “your” favorite president, he is addressing only his supporters, not the country. Polls find Trump’s approval rating to be high among Republicans but it generally ranges between about 35% and 45% among Americans overall.

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TRUMP: “We have lost 500 Billion Dollars a year, for many years, on Crazy Trade with China. NO MORE!” — tweet Friday.

THE FACTS: That’s wrong. When sizing up the trade deficit, Trump always ignores trade in services — where the U.S. runs a surplus with China — and speaks only of goods. Even in that context, he misstated the imbalance.

The U.S. trade deficit with China last year was $378.6 billion, not $500 billion.

On goods alone, the deficit was $419.2 billion.

Trump is also misleading when he puts the deficit in that ballpark for many years. It’s true the imbalance has long been lopsided. But the U.S. Trade Representative’s Office notes that exports of goods to China have increased by nearly 73% since 2008 and U.S. exports to China overall are up 527% since 2001.

Nor is the trade gap a “loss” in a pure sense. U.S. consumers and businesses get electronics, furniture, clothing and other goods in return for their money. They are buying things, not losing cash.

TRUMP: “Tariffs will bring in FAR MORE wealth to our Country than even a phenomenal deal of the traditional kind. Also, much easier & quicker to do. Our Farmers will do better, faster, and starving nations can now be helped. Waivers on some products will be granted, or go to new source!” — tweet Friday.

THE FACTS: In addition to repeating the canard that China pays the tariffs, he’s failing to account for the damage that tariffs can do.

By most private estimates, a trade war leads to slower growth rather than the prosperity that Trump is promising. The president’s tweet also goes beyond past claims that tariffs are simply a negotiating tactic to force better terms with China. Trump appears to be suggesting that a tariff increase would generate revenues that could then be spent on farm products and infrastructure, something that might in theory require support from Congress.

But on their own, tariffs are a clear drag on growth.

Analysts at the consultancy Oxford Economics estimate that implementing and maintaining the latest increase would trim U.S. gross domestic product by 0.3%, or $62 billion, in 2020. This would be equal to a loss of about $490 per household.

Economists at Nomura note that gross domestic product this year could take a hit of as much as 0.4% if Trump expands the taxes to all Chinese imports as business confidence slumped and financial conditions tightened.

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ECONOMY

TRUMP: “And our unemployment numbers are the best in 51 years. And for certain groups, … women is now 71 years.” — remarks Monday to the U.S. Military Academy football team.

THE FACTS: The unemployment rate for women is solid, but it’s not the best in 71 years.

According to the Labor Department, the women’s unemployment rate fell last month to 3.1%. That’s just the lowest since October 1953, or 66 years ago, when it also was 3.1%. The lowest on record was 2.4% in May 1953.

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TRUMP, boasting that his economic record has delivered the “highest income ever in history for the different groups — highest income.” — Panama City Beach, Florida, rally Wednesday.

THE FACTS: Not so. He did not achieve the best income numbers for all the racial groups. Both African Americans and Asian Americans had higher income prior to the Trump administration.

The median income last year for a black household was $40,258, according to the Census Bureau. That’s below a 2000 peak of $42,348 and also statistically no better than 2016, President Barack Obama’s last year in office.

Many economists view the continued economic growth since the middle of 2009, in Obama’s first term, as the primary explanation for recent hiring and income gains. More important, there are multiple signs that the racial wealth gap is now worsening even as unemployment rates have come down.

As for Asian Americans, the median income for a typical household last year was $81,331. It was $83,182 in 2016.

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RUSSIA INVESTIGATION

TRUMP, on his son Donald Trump Jr., who was subpoenaed by the GOP-led Senate intelligence committee to answer additional questions: “My son was totally exonerated by Mueller.” — remarks to reporters Thursday.

THE FACTS: The report does not exonerate Trump Jr.

Special counsel Robert Mueller looked into a potential criminal conspiracy between Russia and the Trump campaign and said the investigation did not collect sufficient evidence to establish criminal charges on that front.

For example, the report cited the case of a June 2016 Trump Tower meeting involving Trump Jr. and a Russian lawyer who was said to have dirt on Democratic presidential candidate Hillary Clinton. Mueller said he considered bringing charges against Trump’s son and others but ultimately wasn’t sure if he could prove “beyond a reasonable doubt” that they knew the actions were illegal. The meeting had raised questions about whether Trump Jr. and others violated the federal ban on foreign contributions to American political campaigns.

Mueller noted some Trump campaign officials, including Trump Jr., had declined to testify while others had provided incomplete or false testimony, making it difficult to get a complete picture of what happened during the 2016 campaign.

The special counsel wrote that he “cannot rule out the possibility” that unavailable information could have cast a different light on the investigation’s findings.

TRUMP, on Mueller’s report: “No collusion. No obstruction. No anything. Two years on a witch hunt.” — Florida rally Wednesday.

TRUMP: “So this comes back and it comes back totally exonerating Donald Trump and a lot of other people. ” — remarks Thursday.

THE FACTS: He’s incorrect to say Mueller’s investigation did not find anything; it found plenty. Nor does the report “totally” exonerate Trump, instead specifically leaving open the question of whether his efforts to undermine the Russian investigation might have obstructed justice.

The two-year investigation produced charges against nearly three dozen people, among them senior Trump campaign operatives and 25 Russians, as it shed light on a brazen Russian assault on the American political system.

The investigation did not establish a criminal conspiracy between the Trump campaign and Russia and it reached no conclusion on whether Trump obstructed justice. Yet it described his campaign as eager to exploit the release of hacked Democratic emails to hurt rival Hillary Clinton and it exposed lies by Trump aides aimed at covering up their Russia-related contacts.

According to the report, Mueller’s team declined to make a prosecutorial judgment on whether to charge partly because of a Justice Department legal opinion that said sitting presidents shouldn’t be indicted.

Instead, the report factually laid out instances in which Trump might have obstructed justice, leaving it open for Congress to take up the matter or for prosecutors to do so once Trump leaves office.

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HURRICANE AID

TRUMP: “Puerto Rico got $91 billion and I understand they don’t like me. It’s the most money we’ve ever given to anybody. We’ve never given $91 billion to a state.” — Florida rally.

TRUMP: “Puerto Rico has been given more money by Congress for Hurricane Disaster Relief, 91 Billion Dollars, than any State in the history of the U.S.” — tweet Monday.

THE FACTS: His number is wrong, as is his assertion that the U.S. territory has set some record for federal disaster aid. Congress has so far distributed only about $11 billion for Puerto Rico, not $91 billion.

He’s stuck to his figure for some time. The White House has said the estimate includes about $50 billion in expected future disaster disbursements that could span decades, along with $41 billion approved.

That $50 billion in additional money is speculative. It is based on Puerto Rico’s eligibility for federal emergency disaster funds for years ahead, involving calamities that haven’t happened.

That money would require future appropriations by Congress.

Even if correct, $91 billion would not be the most ever provided for hurricane rebuilding efforts. Hurricane Katrina in 2005 cost the U.S government more than $120 billion — the bulk of it going to Louisiana.

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IMMIGRATION

TRUMP, claiming countries are taking advantage of the U.S. diversity visa lottery program: “They’re giving us some rough people.” — Florida rally.

THE FACTS: A perpetual falsehood from the president. Countries don’t nominate their citizens for the program. They don’t get to select people they’d like to get rid of.

Foreigners apply for the visas on their own. Under the program, citizens of countries named by the U.S. can bid for visas if they have enough education or work experience in desired fields. Out of that pool of qualified applicants, the State Department randomly selects a much smaller pool of tentative winners. Not all winners will have visas approved because they still must compete for a smaller number of slots by getting their applications in quickly.

Those who are ultimately offered visas still need to go through background checks, like other immigrants.

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VETERANS

TRUMP, describing how veterans used to wait weeks and months for a VA appointment: “For the veterans, we passed VA Choice. … (Now) they immediately go outside, find a good local doctor, get themselves fixed up and we pay the bill.” — Florida rally.

THE FACTS: No, veterans still must wait for weeks for a medical appointment.

While it’s true the VA recently announced plans to expand eligibility for veterans in the Veterans Choice program, it remains limited due in part to uncertain money and longer waits.

The program currently allows veterans to see doctors outside the VA system if they must wait more than 30 days for an appointment or drive more than 40 miles to a VA facility. Under new rules to take effect in June, veterans will have that option for a private doctor if their VA wait is only 20 days (28 for specialty care) or their drive is only 30 minutes.

But the expanded Choice eligibility may do little to provide immediate help.

That’s because veterans often must wait even longer for an appointment in the private sector. In 2018, 34 percent of all VA appointments were with outside physicians, down from 36 percent in 2017. Then-Secretary David Shulkin said VA care was “often 40 percent better in terms of wait times” compared with the private sector.

Choice came into effect after some veterans died while waiting months for appointments at the Phoenix VA medical center.

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TRUMP, on the Choice program: “It’s a great thing for our veterans. They’ve been trying to get it passed for 44 years. We got it passed.” — Florida rally.

THE FACTS: He’s incorrect. Congress approved the private-sector Veterans Choice health program in 2014 and President Barack Obama signed it into law. Trump is expanding it.

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CROWD SIZE

TRUMP, on Democrat Beto O’Rourke’s crowd size at a Texas rally before he launched his presidential campaign: “He had like 502 people.” — Florida rally.

THE FACTS: Trump sells short O’Rourke’s crowd, though it has grown in his mind since he claimed the Democrat only got 200-300 at his El Paso gathering in February. Trump had a rally there the same day.

O’Rourke’s march and rally drew thousands. Police did not give an estimate, but his crowd filled nearly all of a baseball field from the stage at the infield to the edge of outfield and was tightly packed.