WASHINGTON — In the rough-and-tumble of a town hall-style debate, not all of the presidential candidates’ claims stood up to scrutiny Tuesday night.

Yet again, President Barack Obama claimed that ending the Afghanistan and Iraq wars makes money available to “rebuild America,” even though it doesn’t. Republican Mitt Romney actually corrected some of the errant claims he’s made before, while stretching the facts on the auto bailout he opposed. A look at some of their claims:

Obama: “Let’s take the money that we’ve been spending on war over the last decade to rebuild America, roads, bridges, schools. We do those things, not only is your future going to be bright, but America’s future is going to be bright as well.”

The facts: What Obama didn’t mention is that much of the money that has been paying for the wars in Iraq and Afghanistan was borrowed. In fact, the government borrows nearly 40 cents for every dollar it spends.

Romney: “I know he keeps saying, ‘You want to take Detroit bankrupt.’ Well, the president took Detroit bankrupt. You took General Motors bankrupt. You took Chrysler bankrupt. So when you say that I wanted to take the auto industry bankrupt, you actually did. And I think it’s important to know that that was a process that was necessary to get those companies back on their feet, so they could start hiring more people. That was precisely what I recommended and ultimately what happened.”

The facts: What Romney recommended did not happen, and his proposed path probably would have forced General Motors and Chrysler out of business. He opposed using government money to bail out the automakers, instead favoring privately financed bankruptcy restructuring. But the automakers were bleeding cash and were poor credit risks. The banking system was in crisis, so private loans weren’t available. Without government aid, both companies probably would have gone under and their assets sold.

Obama: “And what I want to do is build on the 5 million jobs that we’ve created over the last 30 months in the private sector alone.”

The facts: As he has done before, Obama is cherry-picking his numbers to make them sound better than they really are. He ignores public-sector job losses that have dragged down overall job creation. Also, he chooses just to mention the past 30 months. That ignores job losses during his presidency up until that point. According to the Labor Department, about 4.5 million total jobs have been created during the past 30 months. But some 4.3 million jobs were lost during the earlier months of his administration. At this point, Obama is a net job creator, but only marginally.

Romney: “I’m going to bring rates down across the board for everybody, but I’m going to limit deductions and exemptions and credits, particularly for people at the high end, because I am not going to have people at the high end pay less than they’re paying now.”

The facts: Romney is proposing to cut all income tax rates by 20 percent, eliminate the estate tax and the alternative minimum tax, maintain and expand tax breaks for investment income, and do it all without adding to the deficit or shifting the tax burden from the wealthy to the middle class. He said he would pay for the tax cuts by reducing or eliminating tax deductions, exemptions and credits.

The Tax Policy Center, a Washington research group, said in a study that the proposed tax cuts would reduce federal tax revenues by about $5 trillion during 10 years and that there aren’t enough tax breaks for the wealthy to make up the lost revenue, so the proposal would either add to the deficit or shift more of the tax burden on to the middle class.

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