In this Oct. 16, 2018 photo, President Donald Trump speaks during an interview with The Associated Press in the Oval Office of the White House in Washington. (AP Photo/Evan Vucci)

In this Oct. 16, 2018 photo, President Donald Trump speaks during an interview with The Associated Press in the Oval Office of the White House in Washington. (AP Photo/Evan Vucci)

WASHINGTON (AP) — President Donald Trump inflated the projected benefits of an arms deal with the Saudis as he defended his wait-and-see attitude about Saudi complicity in the disappearance of a journalist whose apparent murder has sparked world outrage.

On immigration enforcement, the president made the unsubstantiated claim that migrants are being paid to mass at the border and somehow disrupt the Nov. 6 elections in the United States. This claim followed his distortions in an Associated Press interview about climate change and the Russia investigation.

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A look at how some of his words over the past week stack up with the facts:

MIGRANTS

TRUMP, on a caravan of Central American migrants trying to reach the U.S.: “A lot of money’s been passing through people to come up and try to get to the border by Election Day because they think that’s a negative for us.” — Montana rally Thursday.

TRUMP on the caravan: “Can you believe this, and what Democrats are allowing to be done to our Country?” — tweet Thursday.

THE FACTS: Trump was riffing off of an unsupported allegation by GOP Rep. Matt Gaetz of Florida that people were being paid in Honduras to join the caravan and “storm the border @ election time,” as Gaetz tweeted.

Gaetz tweeted a video on Wednesday of men handing out money to people standing in a line, without evidence that it illustrated his claim. Questioned about the video’s origin, Gaetz posted a correction on Twitter, saying, “This video was provided to me by a Honduran government official. Thus, I believed it to be from Honduras.”

Neither man has produced evidence that the migrants are being paid to come to the border.

Mexico’s government says migrants with proper documents can enter Mexico and those who don’t either have to apply for refugee status or face deportation.

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SAUDI ARMS DEAL

TRUMP: “Frankly they have a tremendous order — $110 billion. Every country in the world wanted a piece of that order. We got all of it. And what are we going to do? Again, I’ve had some senators come up and some congressmen that said, ‘Well, you know, sir, I think what we should do is we should not take that order.’ I said, ‘Who are we hurting? It’s 500,000 jobs.’” — interview Wednesday with Fox Business News.

TRUMP, on possible action against Saudi Arabia: “I’ll be working on this with Congress. ... But I would prefer that we don’t use as retribution canceling $110 billion worth of work, which means 600,000 jobs. ... I went there to get that order.” — remarks Friday at a defense event in Arizona.

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THE FACTS: Trump’s wrong to suggest that he has $110 billion in military orders from Saudi Arabia. A far smaller amount in sales has actually been signed. His State Department has also estimated much fewer U.S. jobs than Trump’s figure of 500,000 to 600,000, projecting “potentially tens of thousands.”

Details of the $110 billion arms package, partly negotiated under the Obama administration and agreed upon in May 2017, have been sketchy. At the time the Trump administration provided only a broad description of the defense equipment that would be sold. There was no public breakdown of exactly what was being offered for sale and for how much.

The Congressional Research Service described the package as a combination of sales proposed by Obama and discussed with Congress and new sales still being developed.

The Pentagon said this month that Saudi Arabia has signed “letters of offer and acceptance” for only $14.5 billion in sales, including helicopters, tanks, ships, weapons and training. Those letters, issued after the U.S. government has approved a proposed sale, specify its terms.

Regarding economic impact, Trump’s claim of about 500,000 jobs involved — he later upped that figure to 600,000 — is questionable given the tenuous nature of the orders. A May 20, 2017, State Department fact sheet on the proposed $110 billion deal estimated it could end up “potentially supporting tens of thousands of new jobs in the United States.”

Trump’s repeated claims that he’s signed $110 billion worth of new arms sales to Riyadh are “just not true,” said Bruce Riedel, a senior fellow at Brookings Institution and former CIA and Defense Department official. “Very little has changed hands.”

Trump has pledged unspecified “severe punishment” should the U.S. determine Saudi involvement in the disappearance of journalist Jamal Khashoggi, who had written columns critical of Saudi Crown Prince Mohammed bin Salman. But Trump has said he does not want to halt the arms sale to Saudi Arabia because it would harm U.S. manufacturers. Saudi Arabia is indeed a major U.S. ally and arms customer.

Trump on Friday called Saudi Arabia’s announcement that suspects in Khashoggi’s death are in custody a “good first step.” Saudi Arabia has claimed that Khashoggi was killed in a “fistfight” at the Saudi Consulate in Istanbul.

Trump said that before he decided what to do next, he wanted to talk to Saudi Crown Prince Mohammed bin Salman

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MONTANA SENATE RACE

TRUMP, speaking about the failed nomination of White House doctor Ronny Jackson to be Veterans Affairs secretary: “Ever since his vicious and totally false statements about Admiral Ron Jackson, the highly respected White House Doctor for Obama, Bush & me, Senator John Tester looks to be in big trouble in the Great State of Montana! He behaved worse than the Democrat Mob did with Justice K!” — tweet Wednesday.

THE FACTS: Trump misleads by seeking to place the blame for Jackson’s failed nomination entirely on Tester, the top Democrat on the Senate Veterans Affairs Committee. It also remains unclear whether the late-surfacing allegations against Jackson are “totally false” because the Pentagon inspector general is continuing to review some of them.

Jackson, a Navy rear admiral, withdrew his nomination in April after Tester released results of committee interviews he conducted with military personnel who raised questions about Jackson’s prescribing practices and leadership ability. The interviews were done with the knowledge and support of Sen. Johnny Isakson, R-Ga., chairman of the committee considering Jackson’s nomination.

The time period covered Jackson’s tenure as a White House physician dating to 2006 and involved his current and former colleagues who served in both Republican and Democratic administrations.

Jackson, who broadly denied allegations of bad behavior, had already faced tough questions from several committee Republicans about whether he had the experience to manage the massive VA.

The allegations were referred to the Pentagon’s inspector general for evaluation. After an initial assessment and review, the inspector general’s office in June decided a formal investigation was warranted. That probe is continuing, according to the office.

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CLEANEST AIR

TRUMP: “I want the cleanest air on the planet and our air now is cleaner than it’s ever been.” — AP interview Tuesday.

THE FACTS: He’s wrong about the air being the cleanest ever, according to his own administration. While the air generally has been getting cleaner since the 1970s, the downward trend in pollution has made a bit of a U-turn since Trump took office.

His Environmental Protection Agency released data that showed traditional air pollution — soot and smog — increased in 2017 and that the air is not the cleanest it has ever been.

The days with an unhealthy number of small pollution particles, often called soot and linked to heart and lung problems and deaths, jumped from 2016 to 2017 in 35 major metropolitan areas. In 2017, there were 179 unhealthy soot days, up 85 percent from 97 in 2016. Last year had the most unhealthy soot days since 2011.

The number of days with unhealthy smog levels was down from 2016, but higher than 2015, 2014 and 2013.

The number of days when the air quality index was unhealthy was 729 in 2017. It’s higher than a year because it counts each city’s unhealthy reading on a certain day as one and there are numerous cities involved. Last year’s level was the highest since 2012 and a 21 percent increase over the cleanest air in 2014.

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CLIMATE CHANGE

TRUMP, when asked about a dire U.N. report this month on climate change that said dangerous warming has already happened and that with each degree, the many harms to Earth will get even more treacherous: “No, no. Some say that and some say differently, I mean you have scientists on both sides of it.” — AP interview Tuesday.

THE FACTS: He’s wrong to suggest the scientific community is substantially split. Scientists from around the world wrote the recent report, and it was unanimously accepted by government representatives around the world, including in the United States, said Cornell University climate scientist Natalie Mahowald, a lead author of the report.

The Trump administration last year also released the National Climate Assessment, which painted a similar picture.

University of Illinois climate scientist Donald Wuebbles, a lead author of that national report, emailed that “there is no debate AT ALL going on about this within the scientific community.”

“Trump might as well be saying that there are scientists on ‘both sides of the gravity debate,’” Pennsylvania State University climate scientist Michael Mann said in an email. “Dangerous climate change impacts are already apparent. Of course there are uncertainties. There always are. There are uncertainties in the science of gravity (we have never measured a graviton, the fundamental unit of gravity). That doesn’t make it safe to jump off a cliff.”

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IMMIGRATION

TRUMP: “We have the worst laws in the history of the world on immigration and we’re getting them changed one by one. We’ve made a lot of progress in the last couple of weeks even, but we’re getting them changed one by one.” — AP interview Tuesday.

THE FACTS: He’s actually failed to achieve changes in immigration laws. All the immigration-related changes pushed by his administration were done by executive order, not legislation, or through policy shifts such as the zero tolerance policy that criminally prosecuted anyone caught crossing illegally and gave rise to family separations. The administration also has used regulations to tighten the rules on how immigrants can receive public benefits. Immigration legislation has failed despite Republican control of the White House and both houses of Congress.

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TRUMP, on the separation of children from their parents at the border: “Now President Obama had the same law. He did the same thing.” — AP interview Tuesday.

THE FACTS: Obama did not do the same thing as a matter of policy. It’s true the underlying laws were the same. But the Trump administration mandated anyone caught crossing the border illegally was to be criminally prosecuted. The policy meant adults were taken to court for criminal proceedings, and their children were separated and sent into the care of the Health and Human Services Department, which is tasked with caring for unaccompanied migrant children. The zero tolerance policy remains in effect, but Trump signed an executive order June 20 that stopped separations.

Jeh Johnson, Obama’s homeland security secretary, told NPR there may have been unusual or emergency circumstances when children were taken from parents but there was no such policy.

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TRUMP: “And in fact the picture of children living in cages that was taken in 2014 was a picture of President Obama’s administration and the way they handled children. They had the kids living in cages. They thought it was our administration and they used it, and then unbeknownst to them and the fake news they found out, ‘Oh my God, this is a terrible situation.’ This was during the Obama administration.” — AP interview Tuesday.

THE FACTS: He’s right. Images that circulated online during the height of Trump’s family separations controversy were actually from 2014 under the Obama administration. But circumstances for some children have not changed. In June, an Associated Press reporter was part of a group that visited a U.S. Border Patrol holding facility, where hundreds of children were waiting in a series of cages created by metal fencing. One cage had 20 children inside, scattered around were bottles of water, bags of chips and large foil sheets intended to serve as blankets. The cages in each wing opened out into common areas to use portable restrooms.

The children both in 2014 and 2018 were separated temporarily from their parents in the facilities, placed in areas by age and sex for safety reasons.

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RUSSIA INVESTIGATION

TRUMP, about special counsel Robert Mueller’s Russia investigation: “It’s a tremendous waste of time for the president of the United States. To think that I would be even thinking about using Russia to help me win Idaho, we’re using Russia to help me win the great state of Iowa or anywhere else is the most preposterous, embarrassing thing.” — AP interview Tuesday.

THE FACTS: Trump may be right that he did not need a boost in Idaho and Iowa, states he won in 2016 with comfortable margins of 31 percentage points and 9 percentage points, respectively. But the notion of Russia-backed activities on his behalf “anywhere else” in the U.S. is not far-fetched, according to an indictment in February by Mueller.

The indictment accuses 13 Russians and three Russian entities of seeking to help Trump defeat Democrat Hillary Clinton by running a hidden social media trolling campaign and seeking to mobilize Trump supporters at rallies while posing as American political activists in “purple states like Colorado, Virginia and Florida.” According to the indictment, the surreptitious campaign was organized by the Internet Research Agency, a Russian troll farm financed by companies controlled by Yevgeny Prigozhin, a wealthy businessman with ties to President Vladimir Putin.

The indictment says the defendants commonly referred to targeting more closely divided “purple states” after being advised by a Texas-based grass-roots organization in June 2016 to focus efforts there.

The indictment details contacts targeting three unidentified officials in the Trump campaign’s Florida operation. In each instance, the Russians used false U.S. personas to contact the officials. The indictment doesn’t say if any of them responded.

Trump lost by nearly 2.9 million votes in the popular vote to Clinton, but captured the needed Electoral College votes to win the presidency after prevailing in politically divided states including Florida, Michigan, Pennsylvania and Wisconsin.

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TRUMP, on his former personal lawyer, Michael Cohen: “By the way, he was in trouble not for what he did for me; he was in trouble for what he did for himself. You do know that? Having to do with loans, mortgages, taxicabs and various other things, if you read the paper.” — AP interview Tuesday.

THE FACTS: Cohen was definitely in trouble for what he did for Trump. He stated in open court that Trump directed him to arrange payments of hush money to porn star Stormy Daniels and former Playboy model, Karen McDougal, to fend off damage to Trump’s White House bid.

Cohen said one payment was made “in coordination and at the direction of a candidate for federal office,” and the other was made “under direction of the same candidate.”

It is true that Cohen did not identify Trump, but there was no ambiguity in court documents or in his statement.

Cohen’s extraordinary statement at his August plea hearing marked the first time any Trump associate, in open court, has implicated the president himself in a crime.

Trump is, however, correct that other charges which Cohen admitted to didn’t involve the candidate or the campaign and were for tax deception.

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TRUMP: “Do you know these Russian hackers you’re talking about from Moscow? They have nothing to do with me. ... They were hackers from Moscow. Some of them supported Hillary Clinton.” — AP interview Tuesday.

THE FACTS: The Mueller indictment offers no evidence or reason to believe that the Russian effort was intended to help elect Clinton — quite the opposite. Some anti-Trump messaging tied to Russians was indeed disseminated online, but investigators believe the motive was to spread confusion and discord in the campaign, not to elect her.

The pro-Trump efforts identified in the indictment were strategic, on the ground in key states as well as online, and included attempts to make contact with Trump campaign officials. Russian President Vladimir Putin, while denying any involvement in Russian interference, has said he wanted Trump to win.

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Associated Press writers Matthew Pennington, Seth Borenstein, Eric Tucker and Colleen Long contributed to this report.

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