Donald Trump: "Right now, we're the highest taxed country in the world."
The facts: Far from it. The U.S. tax burden pales in comparison with that of other industrialized countries.
Taxes made up 26 percent of the total U.S. economy in 2014, according to the 34-nation Organization for Economic Cooperation and Development. That measure looks at the entire tax burden, which is different than tax rates that can be gamed through loopholes, deductions and credits.
In Sweden, the tax burden is 42.7 percent of the economy. It's 33.6 percent in Slovenia (Trump's wife, Melania, was born in the part of Yugoslavia that became Slovenia). Britain clocks in at 32.6 percent, while Germany's burden is 36.1 percent.
Where is the tax burden lower than the United States?
South Korea, Chile and Mexico.
Ted Cruz, defending his vow to deport 11 million people living in the U.S. illegally: "I would note that in eight years Bill Clinton deported 12 million people. In eight years George Bush deported 10 million people. Enforcing the law. We can do it."
The facts: Statistics from Immigration and Customs Enforcement show that roughly 1.6 million were deported under Bush, not 11 million. Under Clinton, about 870,000 immigrants were deported, not 12 million, according to the Migration Policy Institute. So far, about 2.4 million have been deported under the Obama administration.
To get the swollen figures, Cruz appears to be combining deportations with arrests made by the Border Patrol in the previous administrations, according to the institute.
Trump:: "The insurance companies are getting rich on Obamacare."
The facts: Although some insurance companies are making a profit from their business under President Barack Obama's health care law, the industry's biggest player lost money.
United Health last year reported deep losses from its business on the health law's insurance exchanges and said it will re-evaluate whether it wants to continue in that market. Anthem, the second-largest insurer, said its enrollment in the law's markets fell, and the business has been less profitable than expected.
Aetna, the third-largest insurer, said it has been struggling with customers who sign up for coverage outside the health law's annual enrollment window and then use a lot of care. This dumps claims on the insurer without providing enough premium revenue to counter those costs.
Some industry analysts say insurers are struggling to attract enough healthy patients, and it's too easy for customers to manipulate the system by doing things like signing up for coverage, using health care, and then stopping premium payments.
A dozen of the 23 nonprofit health insurance co-ops created under the law have folded.
Rubio: "Under Chris Christie's governorship of New Jersey, they've been downgraded nine times in their credit rating. This country already has a debt problem, we don't need to add to it by electing someone who has experience at running up and destroying the credit rating of his state."
Christie: "Incorrect and incomplete information."
The facts: Rubio is right that the state's credit rating has been downgraded nine times since Christie took office, a reflection of concern by the major rating agencies about New Jersey's fiscal health and pension system.
Christie: "The president and his former secretary of state are for paying ransoms for hostages. When (you) do that, you endanger even more Americans around the world to be the subject of this type of hostage-taking and illegal detention."
The facts: President Barack Obama said exactly the opposite in June, when the White House reaffirmed its opposition to paying ransom to terrorist groups that hold American citizens hostage.
The president said such payments only serve to endanger more Americans and finance "the very terrorism that we're trying to stop" — points that Christie actually echoed during the debate.
Though the new White House policy precludes ransom payments by the U.S. government, the Obama administration did leave open the door to communication with hostage-takers — whether by the government, families of victims or third-parties — and said relatives who on their own decide to pay ransom won't be threatened with prosecution.
Cruz: "We will adopt commonsense reforms, No. 1, we'll allow people to purchase health insurance across state lines that will drive down prices and expand the availability of low-cost catastrophic insurance."
The facts: Allowing the interstate sale of health insurance policies is not a new idea, and not the straightforward solution that it may sound.
This long-standing Republican proposal has previously run into opposition from regulators in many states. State insurance and consumer protection regulators say such an approach could trigger a "race to the bottom," allowing skimpy out-of-state policies to undercut benefits that individual states require. Proponents of interstate competition say a basic benefits plan would be spelled out.
Some insurance industry insiders see another complication: Out-of-state companies may not have adequate local networks of hospitals and doctors.
It's a tricky position for Republicans in Washington, who argue broadly (Cruz included) that the federal government should defer to state and local decision-making. On this matter, many states don't want the solution that Republicans are pushing.
Rubio on fighting the Islamic State group: "The Kurds are incredible fighters and they will liberate the Kurdish areas, but Kurds cannot and do not want to liberate and hold Sunni villages and towns."
The facts: The Kurds are overwhelmingly Sunni. Rubio did not distinguish between Sunni Arabs and Sunni Kurds. The areas predominantly held by IS fighters are in Sunni Arab territory. They did infiltrate Kurdish regions in both Iraq and Syria, but it is problematic to paint this picture with a broad sectarian brush.
Cruz:defending his vow to "carpet bomb" to defeat the Islamic State: "When I say saturation carpet bombing, that is not indiscriminate. That is targeted at oil facilities. It's targeted at the oil tankers... It's using overwhelming air power."
The facts: Cruz is trying to rewrite the dictionary, which defines the term as dropping many bombs on a small area to prepare it for advancing ground troops. The U.S. military uses precision-guided bombs against the kinds of specific targets that Cruz is talking about, which also reduce the risk of killing civilians — a goal the U.S. military has embraced under Republican as well as Democratic presidents.