While the war on terrorism dominated much of the debate last night between Vice President Cheney and Senator Edwards of North Carolina, the direct contradictions between the two men were so numerous that many voters may have been left with their heads spinning.

“There is no connection between the attacks of September 11 and Saddam Hussein,” Mr. Edwards said early on in last night’s exchange. “You’ve gone around the country suggesting that there is some connection. There is not…. In fact, any connection with Al Qaeda is tenuous at best.”

The assertions met with a tart reply from Mr. Cheney.

“The senator has got his facts wrong,” the vice president said. “I have not suggested there’s a connection between Iraq and 9/11, but there’s clearly an established Iraqi track record with terror.”

As might be expected, both men shaded the truth somewhat. Mr. Edwards downplayed well-documented links between Al Qaeda and Iraq, while Mr. Cheney was a bit too categorical in describing his earlier remarks on the subject.

In testimony to the Senate Armed Services Committee in March, the then director of central intelligence, George Tenet, said Al Qaeda had “contacts with Iraqi regime members going back to the mid-90s.” Mr. Tenet also said Iraq had provided training and safe haven to groups and individuals with Al Qaeda ties. Last year, Mr. Tenet told Congress “Iraq has, in the past, provided training in document forgery and bomb-making to Al Qaeda. It has also provided training in poisons and gases to two Al Qaeda associates.”

Several figures in the administration have recently muddied the waters on this subject, including Defense Secretary Rumsfeld. During an appearance in New York on Monday, he said he had seen “no strong, hard evidence” of such a link.

However, he later said he had been misunderstood. Mr. Rumsfeld issued a statement that included a litany of ties he said the CIA had found or suspected between Iraq and Al Qaeda. They included “solid evidence of the presence in Iraq of Al Qaeda members” and “very reliable reporting of senior level contacts between Iraq and Al Qaeda going back a decade.”

For his part, Mr. Cheney has hinted in the past at the possibility of ties between Iraq and the September 11 attacks. In a September 2003 appearance on NBC’s Meet the Press, Mr. Cheney said that success in Iraq would mean that America “will have struck a major blow right at the heart of the base, if you will, the geographic base of the terrorists who have had us under assault for many years, but most especially on 9/11.”

Asked in that interview whether he was surprised that more than two-thirds of Americans believe Saddam Hussein had some role in the September 11, 2001,strikes,Mr.Cheney said he wasn’t. “No, I think it’s not surprising that people make that connection.”

A few days later, President Bush said flatly that he saw no link between Iraq and the 2001 attacks on America.

Both Mr. Edwards and the debate’s moderator, Gwen Ifill of the Public Broadcasting System, said Mr. Cheney opposed sanctions on countries like Iran and Libya while he was CEO of Halliburton. Mr. Edwards went further, charging that Mr. Cheney’s firm did business in Iran and Libya.

“There’s no substance to the charges,” Mr. Cheney replied.

Mr. Cheney’s answer was a bit too dismissive. During the 1990s,he led a near crusade against sanctions that America had imposed on foreign nations.

“Our government has become sanctions-happy,” Mr. Cheney said at a 1998 conference hosted by a libertarian think tank, the Cato Institute. According to an account in the Dallas Morning News, he singled out sanctions against the Iranians as especially counterproductive. Weeks before joining the ticket in 2000, Mr. Cheney told an audience in Canada, “We would like to do more than we’re able to do in Iran at present.” His firm continued to do business in Iran and Libya through overseas-based subsidiaries.

Mr. Cheney said last night that he was critical only of unilateral sanctions and not those imposed multilaterally or by the United Nations. While that does seem to have been the thrust of Mr. Cheney’s earlier critique, there is no evidence that he was pushing for broader efforts to contain Iran, Libya, or other rogue countries. In fact, Mr. Cheney referred to the campaign to open Iran to American business as “my favorite hobby horse.”

While defending his work at Halliburton, Mr. Cheney referred viewers of the debate to a Web site, www.Factcheck.com. He said the site offered a factual and independent assessment of his tenure at the company.

Those who visit that site might be surprised to see this message in large type, “President Bush is endangering our safety, hurting our vital interests and undermining American values.”

Unfortunately for Mr. Cheney, Factcheck.com is owned by a wealthy financier, George Soros. Mr. Soros is intensely committed to Mr. Bush’s defeat and has spent about $20 million to achieve that goal. Mr. Cheney meant to cite Factcheck.org, a site established by the University of Pennsylvania’s Annenberg Center to evaluate claims made in political commercials and other public statements.

At times last night, Mr. Edwards’s remarks ran counter to some of his previous statements.

During the debate, he forcefully rejected Mr. Cheney’s repeated claims that the Democratic presidential nominee, Senator Kerry of Massachusetts, has offered a series of conflicting statements about Iraq.

“John Kerry has been, as have I, been completely consistent about Iraq,” Mr. Edwards declared.

However, earlier this year, when Mr. Edwards was seeking the presidential nomination, he was among those who said Mr. Kerry’s position on the subject had varied.

“It’s not been clear to me,” Mr. Edwards said in January on ABC. “I think he’s said some different things at different points in time. So, I think there’s been some inconsistency.”

Early in the debate, Mr. Cheney spoke about progress in Afghanistan and preparations for the election scheduled to take place later this week. “We’ve got 10 million voters who have registered to vote, nearly half of them women,” he said.

The vice president’s claim about the Afghan voter rolls is essentially true. More than 10 million voters have been registered for the elections scheduled to take place in Afghanistan this week. According to UN figures, approximately 42% of those registered are women. However, in some of the most traditional parts of the country, women account for just 10% of those who have registered.

As expected, Mr. Edwards repeatedly referred to allegations of profiteering by Mr. Cheney’s former company, Halliburton. The firm did receive no-bid contracts that could be worth billions of dollars. In addition, the Halliburton unit that provides services to the military, KBR, has been accused of charging inflated prices for food and fuel.

However, it does not appear that Iraq has been a gold mine for Mr. Cheney’s former company. KBR, formerly known as Kellogg, Brown & Root, is a perennial money-loser. Halliburton’s present CEO said last month that KBR is planning layoffs and may be sold or spun off it its losses don’t turn around. Wall street analysts say KBR’s poor performance has weighed down Halliburton’s stock while the value of similar companies has been soaring.

In one of the harshest exchanges of the debate, Mr. Cheney scoffed at Mr. Edwards’s attendance record in the Senate. “In my capacity as the vice president, I am the president of the Senate, the presiding officer. I’m up in the Senate most Tuesdays when they’re in session. The first time I ever met you was when you walked on the stage tonight,” the vice president said before laying out a series of statistics about votes and meetings Mr. Edwards had missed.

Regular viewers of C-SPAN know that Mr. Cheney, like most vice presidents, rarely visits the Senate chamber. It’s a little surprising that Mr. Edwards and Mr. Cheney did not cross paths prior to last night, but not quite as unusual as the vice president suggested.

The two candidates also traded jabs over the administration’s record on job creation.

“In the last four years, 1.6 million private sector jobs have been lost, 2.7 million manufacturing jobs have been lost,” Mr. Edwards said.

“The data he’s using is old data,” the vice president complained. “We’ve added 1.7 million jobs to the economy.” Both men were technically correct, but ignored important facts that undercut their respective positions.

Mr. Edwards failed to note that many of the job losses are attributable to the economic downturn that followed the September 11 attacks. He also made no mention of the steady growth in payrolls in recent months.

Mr. Cheney took credit for those new jobs, but left out a little-known fact that might startle some free-market devotees who are part of the Republican base. More than a million of the jobs created under the Bush administration have been in the public sector.