President Bush spoke as if Al Qaeda (search) leaves senior positions vacant when its top operatives are taken down, boasting in his debate with John Kerry that three-quarters of the terrorist network's leaders are gone. His Democratic opponent spoke as if only the rich got a tax cut under Bush, when in fact taxpayers in all income groups did.

Self-serving oversimplifications marked the first presidential debate as Bush and Kerry made their case on Iraq and the broad canvas of foreign policy.

Bush twice suggested Al Qaeda is a vastly diminished force at the top, saying at one point that "75 percent of known Al Qaeda leaders have been brought to justice," and at another, Usama bin Laden (search) is "isolated — 75 percent of his people have been brought to justice."

But Al Qaeda is still considered a mortal danger in part because it refills its ranks and leadership. The president was actually referring to deaths or arrests of operatives who powered Al Qaeda when it mounted the Sept. 11 attacks, not those behind the organization today.

Earlier this year, the CIA (search) estimated two-thirds of those leaders were gone. Bush upped the proportion to three-quarters in his national convention speech in August, based on intelligence findings that were not publicly detailed.

Bush also mischaracterized Kerry's position on withdrawing troops from Iraq: "My opponent at one time said, 'Well, get me elected, I'll have them out of there in six months.' "

In fact, Kerry said he would hope to begin a withdrawal in six months, not complete it. His aim would be to finish the withdrawal in four years if conditions allow.

Kerry stretched in accusing Bush of spending too little on homeland security and too much in giving tax cuts to the rich. "This president thought it was more important to give the wealthiest people in America a tax cut rather than invest in homeland security," he said. "And long before President Bush and I get a tax cut — and that's who gets it — long before we do, I'm going to invest in homeland security."

Bush's tax cuts were across the board, not just for rich people like Kerry and himself.

Kerry, as he often does, said the United States has spent $200 billion on the Iraq war.

An analysis by FactCheck.org at the Annenberg School for Communication found that the true cost to be under $120 billion so far and that Kerry reaches his figure by counting money scheduled to be spent next year, money that hasn't been requested yet and money for Afghanistan operations and U.S. cities.

The Democrat apparently misspoke when painting a dark picture of the chaos in Iraq today. He said of Iraq, "we got weapons of mass destruction crossing the border every single day, and they're blowing people up."

He apparently meant terrorists, not weapons of mass destruction, were crossing the border.

He also misspoke when he referred to looking at KGB records in Treblinka Square in a visit to Russia. Treblinka was a Nazi death camp. He meant Lubyanka Square.

Kerry called Bush on another statement — the president's assertion in reference to Iraq that "the enemy attacked us ... and I have a solemn duty to protect the American people."

As Kerry pointed out, Saddam Hussein did not attack the United States. And the administration has backed away from earlier claims of a direct link between bin Laden and Saddam.

Bush blasted Kerry for calling the Iraq invasion the wrong war at the wrong time and said foreign leaders would never follow a president who talked that way. But major U.S. allies opposed the war from before the start.

Kerry may have overstepped in accusing Bush, in essence, of letting bin Laden get away.

"Unfortunately, he escaped in the mountains of Tora Bora," he said. "We had him surrounded. But we didn't use American forces, the best trained in the world, to go kill him. The president relied on Afghan warlords and he outsourced that job too."

There has been no definitive conclusion bin Laden was in the caves of Tora Bora in December 2001, when U.S. and Afghan troops surrounded the complex and U.S. warplanes blanketed the area with bombs. But U.S. military and intelligence officials believe he probably was. And U.S. forces did largely rely on Afghan forces on the ground to go after him.