Washington (CNN) It's been a busy week for President Donald Trump as he settles into the presidency. Here's a look at some of the more eye-opening statements of the week:

Crime in the city

During the Republican Party retreat in Philadelphia this week, Trump made a reference to the city's murder rate.

"Here in Philadelphia, the murder rate has been steady," he said. "I mean, just terribly increasing."

While the murder rate is up in some big cities, Philadelphia is not one of them . Last year, 277 people were murdered in the City of Brotherly Love. That's hardly different from the 280 that were killed in 2015 and way down from the 391 homicides in 2007. To say it is "terribly increasing" is just plain

How many jobs?

When he signed an executive order clearing the way for the construction of the much-delayed Keystone XL pipeline, Trump touted the number of jobs that would be produced by the $8 billion project.

"A lot of jobs -- 28,000 jobs," he said. "Great construction jobs."

But, as CNN's Rene Marsh and Chris Isidore reported , a 2014 State Department report found that only 3,900 workers would be required to build the pipeline over a year's time.

If the work is spread over two years, 1,950 people would get jobs directly related to the pipeline's construction. Once built, the pipeline would only require 35 full-time employees to run it.

TransCanada, the company that has proposed building the pipeline, does not dispute those figures.

Supporters of the pipeline argue that it would also spin off jobs from companies supplying goods and services for its construction. The State Department report does estimate that the project would create an additional 42,000 jobs with an estimated $2 billion in wages.

But that comes out to an average of about $47,000 in pay for each job.

As a result of all of this, we rate Trump's claim of "28,000 great construction jobs" as false.

How bad is it on the border?

As he signed an executive order to begin the process of building a wall on the US-Mexico border, Trump had this to say about the situation on the country's southern frontier: "A nation without borders is not a nation. Beginning today, the United States of America gets back control of its borders, gets back its borders."

But illegal immigration across the southern border has fallen dramatically in recent years.

According to Customs and Border Protection, 415,816 people were caught trying to enter the country illegally in the fiscal year that ended last September. Of those, 408,870 were caught trying to cross the southern border.

That national figure is less than half the 1.1 million people caught on average annually between 1980 and 2008. Border Patrol said the trends in people seeking to illegally cross the border correlates with the trends in apprehensions.

Apprehensions of Mexicans trying to enter the country illegally are near a 50-year low, according to a study by the Pew Research Center.

The falloff in illegal immigration from Mexico is so great that, according to Pew, in recent years, more Mexicans have returned to their country of origin than have tried to come here. The Border Patrol also notes that "far fewer Mexican nationals and single adults are attempting to cross the border without authorization, while far more families and unaccompanied children are fleeing poverty and violence in Central America."

What is different is that "a growing share" of these Central American migrants are surrendering to law enforcement "to seek humanitarian protection" rather than trying to sneak into the US undetected.

We rate Trump's claim that the country has no borders as misleading.

Spicer's first press briefing

After a flame-throwing weekend start to his tenure as White House press secretary, Sean Spicer showed up for his first weekday briefing a good bit tamer. He tossed out a self-deprecating joke about his rough start, then quickly went into a long session which had two advantages over his initial outing: He held more firmly to the truth and he took questions. Here are two of his bigger assertions.

CLAIM 1: CABINET CONFIRMATIONS

Spicer said at this point in President Barack Obama's first term, seven of his cabinet picks had already been confirmed, compared to only two for Trump as of the moment Spicer made the statement. He said the reason is Democrats are "playing political games." His math is correct and that makes the numeric claim true, although Democrats say the cause of the delay is some of Trump's nominees being slow about submitting their ethics paperwork.

CLAIM 2: OBAMACARE

Spicer said the reason for repealing and replacing Obamacare is simple: the competition among providers, which was supposed to bring prices down, has never materialized.

"You go around the country and look market after market, they are down to one plan. That's not what the American people were promised. Not only that, but in many cases, you are seeing rates go up 10, 15, 20, 30, 50%."

Five states have only one insurer, as do about one-third of counties nationwide, according to the Kaiser Family Foundation. And while some premium prices fell, the average monthly premium for the 2017 benchmark "Silver" plan rose 22% ... with plenty of plans rising in the 10% to 50% range.

This claim is also true.