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.
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 Morsi. 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."
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 Muslim Brotherhood has never appeared on that list.
Verdict: False.
Reality Check: Cruz on Wall Street Journal article on Arizona immigration
By Tami Luhby, CNNMoney
"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 non-emergency 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
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 air strikes have occurred in and around the ISIS de-facto capital of Raqaa, 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 Raqaa 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 Raqaa.
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 U.S. dropped bombs in central Mosul, Iraq, 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
Cruz appeared to suffer from a bit of amnesia when referring to a 2009 shooting at Fort Hood, which he said was located 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 laws 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.
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.
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.
CNN's Katelyn Newman, Justin Gamble and Christian Sierra contributed to this report.
