WASHINGTON (AP) — While speaking in defense of his mental capabilities, President Donald Trump said the question of collusion between his 2016 campaign and Russians is a dead issue, which it isn't. He also said the mandate to buy health insurance or pay a fine is gone — another premature death announcement.

Trump's series of tweets Saturday, as he lashed out at a new book questioning his smarts, took a scattershot approach to the facts, as did his words later to reporters at Camp David. All of this capped a week in which he took unearned credit for safe skies, exaggerated progress in advancing care for veterans and saw his EPA boast about completing pollution clean-ups that were carried out when Barack Obama was president.

A look at those statements and more:

TRUMP: "I guess the collusion now is dead because everyone found that, after a year of study, there's been absolutely no collusion. There has been no collusion between us and the Russians." — to reporters at Camp David

TRUMP tweet: "Now that Russian collusion, after one year of intense study, has proven to be a total hoax on the American public, the Democrats and their lapdogs, the Fake News Mainstream Media, are taking out the old Ronald Reagan playbook and screaming mental stability and intelligence."

THE FACTS: Although he is free to deny that it happened, Trump has no standing to assert that collusion has been ruled out. The special counsel's investigation into Russian meddling in the 2016 election and Russian contacts with Trump's team is continuing and it's premature to say "everyone found" there was nothing.

The probe has not publicly established that Moscow and the Trump team colluded — or that they didn't. The same is true of other potential misdeeds, like obstruction of justice. Trump has often stated that even Democratic leaders have stated there was no collusion. In fact, they have only said that proof has not yet emerged.

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TRUMP: "Don't forget the fact that the individual mandate — such a horrible thing for so many people— was terminated." — to reporters Saturday.

THE FACTS: It's not over until it's over — in 2019. Until then, people who don't get health insurance coverage are still subject to fines. That's unless lawmakers act sooner to relieve people of that responsibility.

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TRUMP: "Since taking office I have been very strict on Commercial Aviation. Good news - it was just reported that there were Zero deaths in 2017, the best and safest year on record!" — tweet Jan. 1.

THE FACTS: It's been 4½ years since the last deaths involving a scheduled passenger airline in the U.S. Three passengers died in the crash of an Asiana Airlines plane while landing at San Francisco International Airport in July 2013. It's been almost nine years since the last fatalities involving a U.S.-registered, scheduled passenger airline in the United States. That was a Colgan Air plane that crashed on approach to Buffalo, New York, in February 2009, killing all 49 on board and a man on the ground.

Last year was notable for having no commercial passenger jet deaths worldwide, although there were two fatal regional airline crashes involving small turboprop planes in Angola and Russia. There were also fatal accidents involving cargo airliners.

What's Trump got to do with any of this?

His administration has instituted additional screening of passengers and their personal electronic devices at foreign airports with flights to the U.S., to prevent terrorist attacks. But there have been no new major safety regulations imposed on passenger airlines as Trump rounds out his first year in office. Indeed, he's held back a regulation pending from the Obama administration that would ban shipments of rechargeable lithium batteries on passenger planes. Testing has shown that the batteries can self-ignite, creating intense fires and explosions.

The White House cited Trump's initiative to "modernize Air Traffic Control" as justification for his tweet, but that doesn't fly. His proposal to privatize air traffic control isn't in effect, so it had nothing to do with the 2017 safety record. And even its proponents say the idea is not about safety, but rather efficiency.

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TRUMP: "We will not rest until all of America's GREAT VETERANS can receive the care they so richly deserve. Tremendous progress has been made in a short period of time." — tweet Tuesday, with an Instagram link showing eight accomplishments where Trump is "fighting for our veterans."

THE FACTS: The video with catchy music overstates the impact of these steps. Of the eight achievements cited, two are ceremonial proclamations — National Veterans and Military Families Month and National Pearl Harbor Remembrance Day.

Two are pieces of legislation that extended a troubled Veterans Choice program on a temporary basis. This became necessary because the Trump administration repeatedly miscalculated the amount of taxpayer dollars available in its account to pay for care from private doctors outside the VA system when veterans had to endure long waits for treatment at VA medical centers

A fifth claim involves "tele-health," letting doctors practice medicine across state lines using digital technology. Announced in August, it has yet to take full effect because a proposed VA regulation hasn't been completed. It's now being dealt with in legislation that passed the Senate and is going to the House.

A sixth claim refers to legislation that streamlines the appeals process for disability compensation claims within the VA. This step has had limited impact so far because it largely applies to new disability claims, not to most or all of the 470,000 pending claims.

The other two initiatives he listed make it easier for the VA to discipline employees. The department has pointed to more than 1,300 employees who have been fired under Trump's watch. But the pace of dismissals is roughly on par with or a little below that during the Obama administration.

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EPA Administrator SCOTT PRUITT, on EPA claims that it completed — or "delisted" — more Superfund sites last year than Obama's EPA did the year before: "We have made it a priority to get these sites cleaned up faster and in the right way." — news release Tuesday.

THE FACTS: This is a case of people taking credit for other people's work.

The EPA removed seven Superfund sites from its priority list last year, compared with two sites delisted the year before. But records show that construction work at all seven sites hyped by Pruitt's EPA, such as removing soil or drilling wells to suck out contaminated groundwater, was completed years before Pruitt was confirmed as the agency's chief in February. Removing sites from the list is a procedural step that occurs after monitoring data show that remaining levels of harmful contaminates meet cleanup targets, which were often set by EPA decades ago.

An analysis of EPA records by The Associated Press shows that the seven Superfund sites delisted last year fell short of the average pace set under both the administrations of Obama and George W. Bush, even in their opening years.

Trump's proposed 2018 budget seeks to cut the Superfund program by 30 percent. More than 1,300 Superfund sites on EPA's list are at various stages in the cleanup process.

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Associated Press writers Hope Yen and Michael Biesecker in Washington and Jason Dearen in Gainesville, Florida, contributed to this report.