WASHINGTON -- Despite promising "the truth, and nothing else" in his convention speech, Donald Trump presented the nation with a series of previously debunked claims and some new ones Thursday night -- about the U.S. tax burden, the perils facing police, Hillary Clinton's record and more.

A look at some of the Republican presidential candidate's claims and how they compare with the facts:

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TRUMP: "Decades of progress made in bringing down crime are now being reversed by this administration's rollback of criminal enforcement. Homicides last year increased by 17 percent in America's 50 largest cities. That's the largest increase in 25 years."

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THE FACTS: A rollback? President Barack Obama has actually achieved some big increases in spending for state and local law enforcement, including billions in grants provided through the 2009 stimulus. While FBI crime statistics for 2015 are not yet available, Trump's claim about rising homicides appears to come from a Washington Post analysis published in January. While Trump accurately quotes part of the analysis, he omits that the statistical jump was so large because homicides are still very low by historical standards. In the 50 cities cited by the Post, for example, half as many people were killed last year as in 1991.

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TRUMP: "The number of new illegal immigrant families who have crossed the border so far this year already exceeds the entire total from 2015. They are being released by the tens of thousands into our communities with no regard for the impact on public safety or resources."

THE FACTS: The pace of releasing immigrants is driven not by the Obama administration, but by a court ruling. A federal judge ruled last year that the government couldn't hold parents and children in jail for more than 20 days. An appeals court partially rolled that back earlier this month, saying that parents could be detained but children must be released.

By the standard used by the government to estimate illegal border crossings - the number of arrests -- Trump is right that the number in this budget year has already exceeded last year's total. But it's down from 2014.

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TRUMP: "When a secretary of state illegally stores her emails on a private server, deletes 33,000 of them so the authorities can't see her crime, puts our country at risk, lies about it in every different form and faces no consequence - I know that corruption has reached a level like never before."

THE FACTS: Clinton's use of a private server to store her emails was not illegal under federal law. Her actions were not established as a crime. The FBI investigated the matter and its role was to advise the Justice Department whether to bring charges against her based on what it found. FBI Director James Comey declined to refer the case for criminal prosecution to the Justice Department, instead accusing Clinton of extreme carelessness.

As for Trump's claim that Clinton faces no consequence, that may be true in a legal sense. But the matter has been a distraction to her campaign and fed into public perceptions that she can't be trusted. The election will test whether she has paid a price politically.

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TRUMP: "The number of police officers killed in the line of duty has risen by almost 50 percent compared to this point last year."

THE FACTS: Not according to the National Law Enforcement Officers Memorial Fund, which tracks police fatalities daily. The group found that the number of police officers who died as of July 20 is up just slightly this year, at 67, compared with 62 through the same period last year. That includes deaths in the line of duty from all causes, including traffic fatalities.

It is true that there has been a spike in police deaths from intentional shootings, 32 this year compared with 18 last year, largely attributable to the recent mass shootings in Dallas and Baton Rouge. But that was not his claim.

And overall, police are statistically safer on America's streets now than at any time in recent decades.

For example, the 109 law enforcement fatalities in 2013 were the lowest since 1956.

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TRUMP: "Two million more Latinos are in poverty today than when President Obama took his oath of office less than eight years ago. Another 14 million people have left the workforce entirely. ... President Obama has almost doubled our national debt to more than $19 trillion, and growing."

THE FACTS: Trump is playing with numbers to make the economy look worse than it actually is. The sluggish recovery over the past seven years has been frustrating. But with unemployment at 4.9 percent, the situation isn't as bleak as he suggests.

Trump's figure of 14 million who've stopped working since Obama took office comes from the Labor Department's measure of people not in the workforce. It's misleading for three reasons: The U.S. population has increased in that time; the country has aged and people have retired; and younger people are staying in school longer for college and advanced degrees, so they're not in the labor force, either.

A better figure is labor force participation -- the share of people with jobs or who are searching for work. That figure has declined from 65.7 percent when Obama took office to 62.7 percent now. Part of that decrease reflects retirements, but the decline is also a long-term trend.

On national debt, economists say a more meaningful measure than dollars is the share of the overall economy taken up by the debt. By that measure, the debt rose 36 percent under Obama (rather than doubling). That's roughly the same as what occurred under Republican President George W. Bush.

The Hispanic population has risen since Obama while the poverty rate has fallen. The Pew Research Center found that 23.5 percent of the country's 55.3 million Latinos live in poverty, compared with 24.7 percent in 2010.

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TRUMP: "My opponent wants to essentially abolish the Second Amendment."

THE FACTS: Clinton advocates expanding gun control measures -- including expanded background checks, a no-fly, no-buy ban for people on terrorist or no-fly lists, repealing a law that protects gun sellers and manufacturers from legal liabiliyand a reinstatement of the assault weapons ban, but she has not said that she wants to take away guns.

Factcheck.org suggests that the claim may be based on a 2015 speech in which Clinton said that "the Supreme Court is wrong on the Second Amendment, and I am going to make that case every chance I get."

But while that sounds like she's threatening the gun right, Factcheck.org goes on to point out that her comments were strictly limited the 2008 Supreme Court ruling that said the Washington, D.C. handgun ban was unconstitutional.

Clinton has spoken up for Second Amendment rights on several occasions, including in this tweet: