WASHINGTON (AP) — President Donald Trump is living in an alternate reality when it comes to special counsel Robert Mueller's investigation and other controversies swirling around him.

He laments the threat of a "perjury trap" in explaining why he's hesitant to be interviewed by Mueller in the Russia probe, even as Trump's lawyers assert that Mueller had ruled out trying to indict a sitting president.

Trump also makes the head-scratching claim that the crimes of his ex-lawyer, Michael Cohen, are not criminal and falsely suggests that Paul Manafort, the president's former campaign chairman, should be viewed as innocent even after being found guilty on several bank fraud and other charges.

The statements came in a week of distorted truth in which Trump also complained about a politician plagiarizing his slogan despite his history of doing the same, wrongly claimed his tax cuts are the biggest ever and defied data in declaring the U.S. is No. 1 in environmental quality.

A look at his rhetoric and how they compare with the facts:

RUSSIA INVESTIGATION

TRUMP, citing concerns of a "perjury trap": "So if I say something and he (former FBI director James Comey) says something, and it's my word against his, and he's best friends with Mueller, so Mueller might say: 'Well, I believe Comey,' and even if I'm telling the truth, that makes me a liar. That's no good." — interview with Reuters published Aug. 20.

RUDY GIULIANI, TRUMP'S ATTORNEY: "I am not going to be rushed into having him testify so that he gets trapped into perjury." — remarks Aug. 19 on NBC's "Meet the Press."

THE FACTS: They're making a disingenuous claim. Both Trump and his lawyers point to a threat of perjury charges, even as Giuliani has maintained that Mueller's team indicated the special counsel had ruled out the possibility of indicting Trump.

Legal experts generally agree that sitting presidents can't be indicted. Mueller would presumably be bound by Justice Department legal memos from 1973 and 2000 suggesting that a sitting president is immune from indictment and that criminal charges would undermine the ability of the commander in chief to do the job.

Trump and Giuliani falsely suggest that Mueller would be able to easily bring a perjury indictment based solely on Comey's contradictory testimony. In fact, perjury charges are often difficult to prove: Mueller would have to show beyond a reasonable doubt that Trump intentionally lied. A conflicting statement from Trump doesn't rise to a criminal offense if he arguably misunderstood, forgot, misspoke or misremembered information.

Mueller could also prepare a report detailing allegations intended for Congress to act upon as an impeachable offense. But impeachment is a political rather than a legal concept, strongly influenced by whichever party is in control of Congress.

Trump's assertion of a "perjury trap" comes as he and his lawyers have hedged on an interview amid a months-long negotiation over whether and how investigators can question the president on possible obstruction of justice in the Russia probe. Mueller's team has put forward questions including about his firing of Comey last year and his public antagonism of Attorney General Jeff Sessions.

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2016 ELECTION

TRUMP: "You know, they kept saying I had a problem with the women's vote; I get 52 percent in the election." — remarks Friday in Columbus, Ohio.

THE FACTS: No. Trump appears to be citing a figure pertaining to white women only.

Among all women, about 54 percent nationally voted for Democrat Hillary Clinton in 2016, according to exit polls, compared with Trump's 41 percent.

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COHEN AND MANAFORT

TRUMP: "Michael Cohen plead guilty to two counts of campaign finance violations that are not a crime." — tweet Wednesday.

THE FACTS: False. The campaign finance violations are crimes. While it's not a crime to pay someone to keep quiet, the Justice Department says the hush money payments arranged by Cohen to conceal allegations of Trump's extramarital affairs were actually unreported campaign contributions meant to influence the outcome of the election.

That's a critical assertion because it makes the payments subject to campaign finance laws, which restrict how much people can donate to a campaign and bar corporations from making direct contributions.

Though some campaign finance experts suggested before the guilty plea that the payments to two women who say they had sex with Trump could have been arranged for other purposes, such as protecting Trump's personal reputation, Cohen himself acknowledged that the goal was to affect the election and protect Trump's candidacy.

The $150,000 payment to former Playboy model Karen McDougal by National Enquirer publisher American Media Inc. and the $130,000 payment to porn actress Stormy Daniels far exceeded permissible campaign contribution limits.

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TRUMP: "A large number of counts, ten, could not even be decided in the Paul Manafort case. Witch Hunt!" — tweet Wednesday.

THE FACTS: The jury's lack of consensus on 10 of 18 counts hardly makes Manafort an innocent man, or supports the notion that Mueller's investigation is a "witch hunt." Manafort, Trump's former campaign chairman, was found guilty on eight counts, including filing false tax returns and two bank fraud charges that will almost certainly guarantee years of prison for him.

On the 10 other counts, the jury was unable to reach a unanimous verdict; they did not acquit him of those charges. Federal prosecutors have the option to try him again on those charges or accept what they've got.

Manafort faces another trial in Washington next month on separate charges, including conspiracy to defraud the U.S., money laundering and witness tampering.

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POLITICAL CAMPAIGNS

TRUMP: "Bill DeBlasio, the high taxing Mayor of NYC, just stole my campaign slogan: PROMISES MADE PROMISES KEPT! That's not at all nice. No imagination!" — tweet Tuesday.

TRUMP: "'Promises Made, Promises Kept.' They're copying it now, the Democrats." — West Virginia rally Tuesday.

THE FACTS: Trump is a slogan copycat himself. His slogan about promises made and kept was used by President Barack Obama in his 2012 campaign. Republican John Engler used it when he ran for re-election as Michigan governor in 1994.

"Make America Great Again" was used by President Ronald Reagan, preceded by "Let's."

"Drain the swamp" was a mantra of House Democratic leader Nancy Pelosi during the 2006 midterm election campaigns, in what turned out to be Democrats' successful bid to take control of the House.

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CLEAN AIR

TRUMP: "I want clean air. I want crystal clean water. And we've got it. We've got the cleanest country in the planet right now. There's nobody cleaner than us." — West Virginia rally Tuesday.

THE FACTS: The United States does not have the cleanest air on Earth. Not even close.

The Associated Press consulted five databases and reports. Each showed countries with cleaner air both in dangerous small particles and in ozone, which is smog.

For example, the Health Effects Institute's state of global air report found 65 countries with less smog when adjusted for season and population. Those include Sweden, Switzerland, France, Germany, Norway, Canada and Venezuela. And in the more dangerous small particles, or soot, eight countries bested the U.S. Among them were Finland, Sweden and Norway.

Yale's performance index ranks the United States 10th in overall air quality behind Australia, Canada, Denmark, Finland, New Zealand and others. But when it comes to dangerous soot exposure levels, the United States ranked 87th, just behind the Philippines.

When it comes to clean water, the data comes close to supporting Trump. Yale's team took the top countries in the world on drinking water and ranked them all No. 1, including the United States, although there are some technical differences among them.

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TAXES

TRUMP: "It is the biggest tax cut in the history of our country and you people are benefiting by it." — West Virginia rally Tuesday.

THE FACTS: This biggest-ever claim has become one of the president's favorite fabrications.

His tax cuts are nowhere close to the biggest in U.S. history.

It's a $1.5 trillion tax cut over 10 years. As a share of the total economy, a tax cut of that size ranks a lowly 12th, according to the Committee for a Responsible Federal Budget.

Are people already seeing benefits from the tax cuts? Companies definitely are.

Economic growth has picked up this year because of the deficit-financed stimulus. Companies are taking their tax savings and buying back stock at a record pace, according to TrimTabs Investment Research.

But so far, the tax cuts haven't delivered a major shot of financial adrenaline to most families.

One recent estimate by former Treasury Department official Ernie Tedeschi is that the cuts are adding $50 a month to average take-home pay, a figure that falls to $17 a month when higher state and local taxes are included in the estimate.

Nor are the cuts fueling higher wage growth.

The Bureau of Labor Statistics found that wages have dropped in the past 12 months after adjusting for inflation.

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IMMIGRANTS AND CRIME

TRUMP, praising Immigration and Customs Enforcement: "To hear some of the stories going on with MS-13, you wouldn't believe it. And they're doing an incredible job. They're actually liberating towns." — remarks Aug. 20.

TRUMP: "A vote for any Democrat in November is a vote to eliminate immigration enforcement, throw open our borders and set loose vicious predators and violent criminals. They'll be all over our communities. They will be preying on our communities." — West Virginia rally Tuesday.

THE FACTS: Trump suggests that weak border enforcement is contributing to crime committed by MS-13. But the gang actually has many U.S.-born members at this point — people who by virtue of U.S. citizenship can't be denied entry based on their nationality, or deported. The government has not said recently how many members it thinks are citizens and immigrants. In notable raids on MS-13 in 2015 and 2016, most of the people caught were found to be U.S. citizens.

More broadly, Trump overgeneralizes about people who arrive illegally in the U.S. Several studies have shown that immigration does not lead to increased crime.

Foreign-born immigrants are less likely to commit crime than native-born Americans, the research found, but crime rates rise for succeeding generations as the children and grandchildren of immigrants become more like native-born Americans.

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TRUMP: "We have MS-13 on the run. They've poured in here with Obama, we have them on the run." — remarks Tuesday.

THE FACTS: There's no evidence that MS-13 gangs "poured in" during the Obama administration. The Justice Department has said there are about 10,000 MS-13 members in the U.S., the same number as more than a decade ago.

Trump's Justice Department has indirectly credited the Obama administration, in its early years, with putting heavy pressure on the gang. It said, "Through the combined efforts of federal, state and local law enforcement, great progress was made diminishing or severely (disrupting) the gang within certain targeted areas of the U.S. by 2009 and 2010."

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TRUMP: "The new platform of the Democrat Party is to abolish ICE." — remarks Friday in Columbus, Ohio.

TRUMP: "Leading members of the Democrat Party have even launched a campaign to abolish ICE. In other words, they want to abolish America's borders." — remarks Aug. 20.

THE FACTS: While some Democrats in the House and Senate have raised the prospect of eliminating Immigration and Customs Enforcement, no top Democrats in the House or Senate have called for such a move. Those Democrats who have expressed openness to eliminating ICE have said they would not abandon border enforcement, which is largely carried out by Customs and Border Protection.

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Associated Press writers Eric Tucker, Chad Day, Josh Boak, Seth Borenstein and Cal Woodward contributed to this report.

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Health Effects Institute: https://www.stateofglobalair.org/report

Yale's Environmental Performance Index: https://epi.envirocenter.yale.edu/2018-epi-report/introduction

Berkeley Earth's air pollution monitoring: http://berkeleyearth.lbl.gov/air-quality/CountryList.php?mode=5

Institute of Health Metrics and Evaluation: http://www.healthdata.org/

World Health Organization's Urban Ambient Air Pollution: http://www.who.int/phe/health_topics/outdoorair/databases/AAP_database_summary_results_2016_v02.pdf?ua=1

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