Washington (CNN) Ted Cruz, Donald Trump and John Kasich gathered in Milwaukee, Wisconsin, for CNN's Republican Town Hall on Tuesday , and CNN's Reality Check team spent the night putting their statements and assertions to the test.

The team of reporters, researchers and editors across CNN listened throughout the event and selected key statements, rating them true; mostly true; true, but misleading; false; or it's complicated.

Ted Cruz

Reality Check: Cruz on the Muslim Brotherhood

By Ryan Browne, CNN

Cruz slammed President Barack Obama and former Secretary of State Hillary Clinton for their foreign policy with respect to the Middle East, specifically the Obama administration's policy in Egypt, accusing the administration of being glad a "terrorist organization" took over that country.

"We saw a similar thing in Egypt where Obama and Hillary both cheered the toppling of Hosni Mubarak, the head of Egypt," Cruz said. "Egypt was handed over to the Muslim Brotherhood. Mohamed Morsy. The Muslim Brotherhood is a terrorist organization. That was profoundly harmful for U.S. National Security interests. Thankfully President El Sisi is now in charge of Egypt."

The Obama administration did welcome Mubarak's 2011 decision to step down amid widespread public demonstrations that called for the end of his more than 30-year reign with Obama, saying the peaceful protests had "bent the arc of history toward justice once more."

And while the Muslim Brotherhood would eventually win elections in Egypt, is the Muslim Brotherhood a terrorist group?

The Muslim Brotherhood is an Islamist organization with active branches in many Middle Eastern countries. It was founded on the belief that Islam is not simply a religion, but a way of life and advocates for a move away from secularism.

The U.S. State Department currently lists 59 designated foreign terrorist groups. The last group to be added was ISIS' Afghanistan branch. The State Department has also removed 12 terrorist groups from the list.

The Muslim Brotherhood has never appeared on that list.

Soon after the Muslim Brotherhood was ejected from power in Egypt, the interim government of Gen. Abdel Fattah el-Sisi declared the Muslim Brotherhood to be a terrorist group . At the time of the designation, the U.S. opposed the move, with a State Department spokesperson saying, "We are concerned about the current atmosphere and its potential effects on a democratic transition in Egypt."

While Bahrain, Saudi Arabia and the United Arab Emirates have also since designated the Muslim Brotherhood a terrorist group, the vast majority of countries, including the United States, has not.

Verdict: False.

Reality Check: Cruz on Wall Street Journal article on Arizona immigration

By Tami Luhby, CNNMoney

Asked about the importance of immigrant workers to farmers, Cruz once again brought up a Wall Street Journal story that looked at Arizona's crackdown on undocumented workers and the impact on state and business spending.

"Arizona is spending hundreds of millions of dollars less on prisons, on education, on hospitals, for those here illegally. That means that's hundreds of millions of dollars available to take care of U.S. citizens, and also unemployment has gone down and median wages for Americans have gone up in the construction industry, carpentry," Cruz said.

The number of undocumented workers in Arizona dropped by 40% between 2007 and 2012, the Journal writes, citing a Pew Research Center report.

Here's what the Journal article actually said about the economic impact of that decline:

-- The number of students enrolled in intensive English courses in Arizona public schools fell from 150,000 in 2008 to 70,000 in 2012 and has remained constant since. Schooling 80,000 fewer students would save the state roughly $350 million a year, by one measure.

-- Annual emergency-room spending on noncitizens fell 37% to $106 million from $167 million.

-- The annual cost to state prisons of incarcerating noncitizens convicted of felonies fell 11% to $180 million, from $202 million.

-- Wages rose about 15% for Arizona farmworkers and about 10% for construction between 2010 and 2014, according to the Bureau of Labor Statistics.

It's true that the Journal story said that spending on education dropped by hundreds of millions of dollars. But Cruz exaggerates the other claims, so we rate them as false.

The savings from fewer incarcerations and emergency-room visits are much smaller. In fact, it notes that undocumented immigrants cannot receive government benefits, including nonemergency hospital care.

Also, Cruz implies that American citizens are the ones who benefited from rising wages and declining unemployment. However, the story doesn't specify whether pay is rising for legal immigrants or citizens. It noted that some of the low-skilled workers who benefited are native-born Americans.

Reality Check: Cruz on anti-ISIS campaign

By Jamie Crawford, CNN

Ted Cruz said the following about the current military campaign being waged by the United States-led coalition against ISIS: "You can take out their command and control headquarters, you can take out their communication, you can take out their means of transportation, ingress and egress. You can take out their oil fields, you can take out their oil refining capacity, you can take out their infrastructure, you can target their troops and their troop movements. And we're not doing that right now."

While a significant amount of airstrikes have occurred in and around the ISIS de-facto capital of Raqqa, Syria, and its stronghold of Mosul in northern Iraq since the strikes began in August 2014, ISIS still maintains a firm grasp on those two cities. But there has been a significant campaign to deny the group an ability to move equipment and fighters between those two cities and places in between.

In November, Kurdish Peshmerga forces in Iraq, backed up by coalition air support, reclaimed the town of Sinjar from ISIS along with the strategic Highway 47 that runs between Raqqa in Syria and Sinjar, Iraq, and on to Mosul, thereby denying a direct route between the two cities. The coalition has also lent significant air power to back up a push by Kurdish forces in Syria as they pushed ISIS out of the town of al-Shadaadi that sits along a crucial supply route into Raqqa.

In addition to this, the coalition last year embarked on an operation to significantly degrade ISIS's ability to produce and profit from illicit oil production and supply.

As of March 17, the Pentagon says there have been 1,272 airstrikes directed at targets that service ISIS's oil infrastructure. The best estimates say ISIS was producing nearly 50,000 barrels a day in 2014. And it was raking in up to $1.6 million daily, according to the United Nations. It's hard to say exactly how far production and oil revenue have fallen since then. Andreas Krieg, a military expert at King's College London, told CNNMoney earlier this month he thinks output is now closer to 20,000 barrels per day, a figure that is in line with other recent estimates.

The Pentagon also says there have been over 7,000 airstrikes on ISIS fighting positions and over 1,000 staging areas.

In January, the United States dropped bombs in central Mosul, destroying a building containing huge amounts of cash ISIS was using to pay its troops and for ongoing operations. There have been subsequent strikes targeting facilities that ISIS uses to finance its operations and pay its troops.

Verdict: False.

Reality Check: Cruz on 2009 Fort Hood attack

By Lydia O'Neal, CNN

In one of the weirder moments of the night, Ted Cruz appeared to forget where he is from. He referred to a 2009 shooting at Fort Hood as taking place in "my home state of Florida."

It is correct that the attack took place in the junior senator's home state, but he was elected to the U.S. Senate by Texans, not Floridians. While he's spent a lot of time there campaigning, he remains a Texas resident.

Cruz has lived in his birthplace of Alberta, Canada; New Jersey during his undergraduate years at Princeton; Massachusetts during his law school years at Harvard; Virginia during his clerkship at the United States Court of Appeals for the Fourth Circuit; and Washington, D.C., while he clerked for the Supreme Court chief justice and then worked for a private law firm. He also later served the George W. Bush administration.

But he has never lived in Florida, making it hard for him to claim it as his home state.

Verdict: False.

Reality Check: Cruz on NYPD surveillance of Muslim neighborhoods

By Sonam Vashi, CNN

Ted Cruz debated the success of a controversial New York Police Department surveillance program, also called the Demographics Unit. The program began in 2003 and ended in 2014 and used plainclothes officers to monitor conversations and the whereabouts of people in Muslim neighborhoods in the New York region.

Let's look at some of the claims Cruz made during the exchange:

Cruz: "Obama and Hillary both advocate bringing tens of thousands of Syrian Muslim refugees."

false. In September, the White House announced it planned to admit 10,000 Syrian refugees this fiscal year, a significant bump at that point from the 1,500 refugees admitted since the start of the Syrian conflict in 2011. We checked this claim before and found it was. In September, the White House announced it planned to admit 10,000 Syrian refugees this fiscal year, a significant bump at that point from the 1,500 refugees admitted since the start of the Syrian conflict in 2011.

Shortly after that, Secretary of State John Kerry announced that the United States would increase the total number of migrants accepted from all countries to 100,000 in 2017. Many of those additional migrants would likely be Syrian refugees, but it's unclear how many exactly the United States would accept. Therefore, Cruz does not know that Obama or Clinton have advocated bringing "tens of thousands of Syrian Muslim refugees." (Additionally, Syrians practice many faiths, and the United States has not advocated bringing in a specific faith alone).

Cruz later went on to defend the NYPD program's success, saying it was "set up under Mayor Michael Bloomberg to monitor and to work cooperatively with the Muslim community to prevent radicalization and to stop radical Islamic terrorism plots."

The program was set up under Bloomberg, and it aimed to find places where potential terrorists might radicalize to prevent terror plots. This involved gathering information about neighborhood demographics, creating profiles on residents, and building lists of mosque memberships.

The NYPD admitted in 2012 that its program never led to a terrorism investigation by the NYPD, during at least six years of surveillance.

It's also unclear how "cooperative" this program was. Muslim community leaders lambasted the program and its tactics. The NYPD became the subject of two federal lawsuits because of this program, and the department settled both of them, agreeing that it would bolster oversight of its intelligence gathering and create guidelines to avoid religious profiling. One of the lawsuits accused the NYPD of violating the Constitution through religious profiling. The NYPD did not admit engaging in any improper practices, according to the settlement.

When moderator Anderson Cooper asked Cruz to name a case triggered by the program, Cruz responded, "There are a number of cases. It identified a bookstore that was a locus for radicalization and allowed law enforcement to go after that bookstore, and what happened was when Mayor Bill de Blasio got elected, he gave in to political correctness and shut the unit down."

The NYPD program did have some counterterrorism successes, including a case where the Demographics Unit provided a tip on a Brooklyn bookstore, according to The Associated Press . The tip eventually led to the arrest of two men involved in a 2004 plot to bomb a Manhattan subway station. One of the men, Shahawar Matin Siraj, was convicted and sentenced to 30 years in prison in 2007.

true. In another case, the program provided an undercover officer to aid in a 2010 bust of two New Jersey men who attempted to travel overseas to join Al-Shabaab, the Somalian terrorist group. The men were not plotting domestic attacks, and they were convicted in 2013 . Cruz's claim here is

Lastly, Cruz compared America's situation with that in Europe, stating that Islamic terrorists hide in isolated communities. "They're called no-go communities where the law enforcement doesn't engage in those communities," Cruz said. "One in Brussels, Molenbeek, has been a particular incubator for radical Islamic terrorism. Many of these terrorist plots trace back to Molenbeek."

The Molenbeek neighborhood in Brussels has become infamous as a new hotbed of radical jihadism, especially as some of the Paris attackers hailed from this neighborhood. Molenbeek is a working-class district that also faces high unemployment. However, Cruz's assertion that law enforcement doesn't engage in these communities is wrong; police do patrol the neighborhood of Molenbeek and have conducted raids. CNN's Nima Elbagir talked to some Molenbeek residents who felt police actions in their community were abusive, provoking more anti-Belgium sentiments.

While the neighborhood may have a mix of security concerns, asserting that police distinctly avoid such neighborhoods as "no-go zones," or areas that are barricaded under entire terrorist control, is completely false.

Donald Trump

Reality Check: Trump on refugees

By Jamie Crawford, CNN

"Thousands of people are being allowed into this country over short periods of time, coming supposedly from Syria," Trump said. "We have no idea who they are, we have no idea where is their paperwork. They have no paperwork, they have no identification. They're coming into this country, and it's going to be a big, big problem."

While the Obama administration has said it has a goal of admitting 10,000 refugees from Syria before the end of the fiscal year on September 30, the United States has only admitted approximately 1,200 refugees at this point. In fact, U.S. government data show that just under 2,200 refugees from Syria have been admitted to the United States since the civil war in Syria began in March 2011.

The process for Syrians to gain admittance into the United States is actually quite cumbersome comparatively. While the average processing time for refugee applications is 18 to 24 months, applications for Syrians can take significantly longer because of security concerns and difficulties in verifying the information they provide for processing.

Based on Trump's comments that "thousands" of people "supposedly from Syria" have entered the United States with no accounting for who they are, we rate this statement false.

Reality Check: Trump on NATO and terrorism

By Ryan Browne, CNN

While Trump has often criticized the U.S. financial contribution to NATO, on Tuesday he also slammed the alliance for not being involved in counterterrorism and accused it of being "obsolete."

"It was 67 years, or it's over 60 years old," Trump said. "It is -- many countries, doesn't cover terrorism. OK? It covers the Soviet Union, which is no longer in existence. And NATO has to either be rejiggered, changed for the better."

NATO was founded in 1949 during the early days of the Cold War when Western Europe was faced with the threat of military intervention by the Soviet Union.

The organization was founded around the principle of collective defense, a notion enshrined in Article 5 of the NATO founding treaty which stipulates that the member nations "agree that an armed attack against one or more of them in Europe or North America shall be considered an attack against them all."

However, since the end of the Cold War and the collapse of the Soviet Union, NATO has taken on other functions, including intervening to stop genocide in the Balkans during the late 1990s.

NATO members also invoked Article 5 for the first and only time in response to the al Qaeda terrorist attacks of September 11, 2001, on the United States.

This decision enabled NATO to lead the international military intervention in Afghanistan.

In October 2011, NATO also launched Operation Active Endeavor. The ongoing operation involves NATO naval vessels patrolling the Mediterranean and monitoring shipping "to help deter, defend, disrupt and protect against terrorist activity," according to NATO.

The alliance has also taken other efforts in the realm of counterterrorism, including the 2004 establishment of NATO's Defense Against Terrorism Program of Work which aims to develop "technologies to detect, disrupt and defeat terrorists," according to NATO. This involves sharing military innovations to protect troops, civilians and critical infrastructure against suicide attacks, improvised explosive devices (IEDs), rocket attacks against aircraft and helicopters and attacks using chemical, biological or radiological material.

It also provides for the development of rapid response capabilities for the protection of civilian populations and infrastructure in NATO member countries.

NATO also adopted counterterrorism policy guidelines and created a Center for Excellence focused on Defense Against Terrorism.

While NATO is over 65 years old and was established to face the Soviet threat, it has since developed several counterterrorism initiatives, so it does indeed "cover terrorism."

Verdict: False.

Reality Check: Trump says reporter grabbed him

By Chip Grabow, CNN

Trump was asked about the incident involving his campaign manager who was arrested and charged with simple battery earlier Tuesday. Former Breitbart reporter Michelle Fields accused Corey Lewandowski of grabbing her during a campaign event earlier this month in Jupiter, Florida. She filed a police report three days later. Fields' claims that Lewandowski grabbed her with enough force to leave bruises on her arm. Lewandowski and the Trump campaign have denied the allegation.

Tuesday night, Trump defended Lewandowski and disputed the charge. In fact, in his version of the encounter, Trump claimed that the reporter grabbed him.

"Am I supposed to press charges against her? 'Oh, my arm is hurting,' " Trump said facetiously. "My arm is just killing me. It's never been the same." He referenced security camera footage of the incident: "She shouldn't have been touching me. OK? And you saw that she did that. She was grabbing me. Twice."

A review of the video does show Fields approaching Trump; she says she was trying to ask him a question. Lewandowski then comes up from behind her and grabs her left arm to pull her away from the candidate. The camera angle and quality of the video makes it difficult to confirm if Fields may have touched Trump to get his attention.

But the video does not support Trump's claim that Fields grabbed him.

Verdict: False.

Reality Check: Trump on self-funding

By Theodore Schleifer, CNN

Trump conceded that he is not 100% responsible for the money in his campaign coffers, but said the money that he raises from individuals is trivial and comes from knickknacks like "hats and T-shirts."

"I'm in for about $35 million right now. We take the small loans -- the people that send $17.50 or $250, even $1,000," he told Cooper.

"But you solicit those on your website," Cooper responded.

"No, I sell hats and shirts," Trump said, later admitting: "OK, whatever. It's peanuts, OK? It's peanuts."

Trump does indeed have a campaign store as other candidates do, in which voters can buy apparel that campaigns typically profit on. But he does not just sell "hats and shirts" -- he has two prominent "Donate" buttons on his campaign website outside of the online store. So Trump's campaign account has a traditional way to raise money that he at first denied.

Cooper told Trump that he has collected more than $7 million from outside contributors, a third of the total money his campaign has taken in. The GOP front-runner disputed that.

Trump has raised $34.7 million, according to the latest federal election records, including about $24.5 million that he has loaned himself. Trump has actually raised $9.5 million from individual contributors, or more than one-quarter of all the money Trump has raised.

While Trump is right that he has not done the big-money fundraising that undergirds modern political campaigns, only a billionaire would consider the $9.5 million he raised from individuals "peanuts."

Verdict: False.

Reality Check: Trump on San Bernardino

By Kate Grise, CNN

Trump again railed against political correctness, saying that neighbors of the San Bernardino bombers did not report suspicious activity for fear of being accused of racial profiling.

"(The San Bernardino attackers) had bombs on the floor. Many people saw this. Many, many people. Muslims living with them in the same area. They saw that house. They say that," Trump said. "One didn't want to turn -- he said, 'I don't want to turn him in because I don't want to be accused of racial profiling.' He saw bombs all over the apartment, OK? It's just an excuse."

There is no evidence to support Trump's claims.

It is true that 12 pipe bombs and a de facto bomb lab were found in the townhouse where Syed Farook and Tashfeen Malik lived.

It is less clear who Trump describes as Muslim neighbors who allegedly saw the bombs and didn't report them because of fears of profiling.

One of Farook's friends, Enrique Marquez, told police the two had experimented years earlier with making pipe bombs, so he obviously saw some bombs. But Marquez has never indicated that he did not alert authorities about bomb-making because he didn't want be accused of racial profiling.

Marquez has pleaded not guilty to charges of conspiring to provide material support to terrorists, making false statements when buying two rifles, marriage fraud and making a false statement on immigration paperwork.

There are news accounts of two people expressing concern about reporting suspicious activity because they didn't want to be accused of racial profiling. KCBS reported that a man who had been working in the area around the shooters' home, "said he noticed a half-dozen Middle Eastern men in the area in recent weeks, but decided not to report anything since he did not wish to racially profile those people."

In another report from KABC, a neighbor, Aaron Elswick, said that another neighbor noticed that quite a few packages arrived within a short period of time and "they were actually doing a lot of work in the garage. He added that the neighbor "was kind of suspicious" and would have reported it, but she "didn't want to profile" the family.

There are no reports, however, that any of Farook and Malik's neighbors saw "many bombs all over their apartment" or that any of the neighbors who said they saw suspicious activity were Muslims.

Verdict: False.

John Kasich

Reality Check: Kasich on beating Clinton in polls

By Lisa Rose, CNN

John Kasich explained his rationale for remaining in the presidential race after winning just one primary out of 28 state contests so far. The delegate math makes it impossible for Kasich to become the Republican nominee. So the Ohio governor is looking to the polls for light and hope.

"In virtually every national poll, I am the only one that beats Hillary Clinton consistently," Kasich said. "In fact, in the last poll that came out, I was up 11 points."

It's true. In six national polls conducted over the past two weeks, Kasich defeats Clinton by margins that range from 4 points to 11 points. A CNN/ORC poll conducted March 17-20 found Kasich would beat Clinton in a head-to-head matchup by 6 points.

Still, a long, strange series of events would need to take place for the Ohio governor to get matched up against the Democratic candidate in the fall. If Donald Trump and Ted Cruz fail to hit 1,237 delegates, the nominee would be chosen via open balloting at the Republican National Convention in Cleveland in July.

Kasich is banking on the idea that the delegates will embrace him as the most appealing candidate, even though the Republicans in the voting booths thus far don't seem to be as enthusiastic. Kasich's premise hinges on the delegates choosing him as a unity candidate. Then, everyone hugs it out in Cleveland and the Republicans take back the White House in 2017.

It could happen.

Verdict: True.

Reality Check: Kasich on Ohio job creation

By Tami Luhby, CNNMoney

Defending his record as Ohio's governor, John Kasich said his state went from losing 350,000 jobs to gaining 417,000 jobs.

"We were 48th when I became governor, now we're in the top 10," Kasich said.

It's false that Ohio is now among the top 10 in terms of job creation. In fact, it ranked 27th in private sector job creation over the past year, with a 1.78% growth rate, according to Bureau of Labor Statistics data crunched by Arizona State University.

And the Buckeye State has trailed the national rate of private sector employment growth since he took office in January 2011. Nationally, employment is up 11.9%, but in Ohio, it has only grown 9.8%.

Kasich may have been referring to a Gallup Job Creation Index, which lists Ohio as one of five states tied for 10th place. These results, however, were based on a poll, not government employment data.