Separated by five states, two television news outlets and a deep trough of mutual animosity, President Trump and Democrat Joe Biden held dueling town halls Thursday that offered a jarring contrast of their opposing political styles and approaches to major issues like the coronavirus pandemic.

The events — with Trump on NBC from Miami and Biden on ABC from Philadelphia — appeared to be broadcast from entirely different dimensions. The soft-spoken Biden leaned back in a white chair, relaxed and conversational as he hit upon notes of optimism and uplift. Trump’s appearance was heated and at times abrasive, with the candidate leaning forward as he defended his record and challenged the motivations of moderator Savannah Guthrie.

In a rapid-fire 60 minutes, Trump doubted the effectiveness of wearing of masks to prevent viral spread, refused to denounce the baseless QAnon conspiracy theory, repeatedly declined to say whether he was tested for the coronavirus before the last debate and battled with Guthrie, who pressed him with details and a mastery of the facts that some moderators have not possessed when sparring with him.

President Trump and former vice president Joe Biden faced off on Oct. 15 at the same time — on separate networks. Here is a roundup of seven false claims. (The Washington Post)

He said his FBI director, Christopher A. Wray, was not “doing a very good job” because he did not embrace Trump’s false claims of widespread voter fraud. He denounced white supremacy, after being asked why he would not do so in the first presidential debate. And he predicted a “red wave” on Nov. 3, even though many of his campaign officials are skeptical.

In one of the most notable exchanges, he said he did not know about QAnon, a loose-knit online community that was recently banned from Facebook. Supporters of the group, which shares false stories, including ones about Democrats abusing children, regularly appear with signs and apparel at Trump’s rallies.

“They are very strongly against pedophilia, and I agree with that,” he said about the group before attempting to pivot the conversation to talk about left-wing radicals like self-described anti-fascist protesters.

The president said under questioning by Guthrie that his lungs were “infected” during his bout with the coronavirus and that he had a “little bit of a temperature.”

Trump did not answer her repeated questions about whether he was tested on the day of the first debate, as required, and would not say when his last negative test was. “I don’t know. I test all the time.” He said he “probably” took a test on the day of the debate.

“As president I can’t just be locked in a room someplace and not do anything,” he said when asked why he did not often wear a mask. “I can’t be in a basement.”

He also refused to apologize for recently retweeting a false conspiracy theory that holds that the Obama administration faked the death of al-Qaeda leader Osama bin Laden, the mastermind of the Sept. 11, 2001, terrorist attacks, and may have orchestrated the murder of U.S. Special Forces personnel. He said it was a “retweet,” suggesting he was not responsible for its accuracy.

“You’re the president,” Guthrie replied. “You’re not like someone’s crazy uncle who can retweet whatever.” Trump responded by calling the media “so fake and so corrupt,” and said he needed to rely on social media to “get the word out.”

While Trump sparred in Miami, the mood in Philadelphia resembled an academic policy discussion more than a political showdown, as Biden chatted with ABC’s George Stephanopoulos and voters — bantering with some of them, asking if he answered their questions and offering to talk more with at least one voter afterward. Biden reiterated his usual campaign talking points, saying little surprising.

He spoke about taxes, fracking, outreach to Black voters, foreign relations and the pandemic. He was asked three sets of questions about racial justice and two about gay, lesbian and transgender rights.

Biden reiterated the importance of wearing masks, again saying that if he were president he would pressure governors and local leaders to institute mask mandates. He said he would not impose fines for those who refused to take a coronavirus vaccine.

“I am running as a proud Democrat, but I am going to be an American president,” he said. “I am going to take care of those who voted against me as well as those who voted for me. For real. That’s what presidents do. We’ve got to heal this nation.”

He criticized Trump at length for not modeling good behavior by wearing a mask.

“The words of a president matter — no matter whether they’re good, bad or indifferent, they matter,” Biden said. “And when a president doesn’t wear a mask or makes fun of folks like me when I was wearing a mask for a long time, then people say: ‘Well, it must not be that important.’ ”

During the town hall, a Trump campaign adviser, Mercedes Schlapp, mocked the Biden performance on Twitter, saying it felt “like I am watching an episode of Mister Rodgers Neighborhood.”

Biden and Trump were both on home turf Thursday night — Biden in the state where he grew up and the city where his campaign is headquartered, Trump in the state that he now claims as his official residence. As Pennsylvanians took turns introducing themselves and asking Biden questions, the former vice president often responded with how well he knows the city or town where they live.

The separate town halls took place on what would have been the night of the second scheduled presidential debate, from which Trump withdrew after the Commission on Presidential Debates announced plans to hold it remotely as a health precaution related to the president’s recent coronavirus infection. After a three-night hospital stay, Trump’s doctor has said he has tested negative for the virus and is no longer contagious.

The first one-on-one debate between Biden and Trump, on Sept. 29, was widely seen as a chaotic and uninformative event, reflective of the nation’s growing polarization and a declining level of civil discourse. Trump repeatedly interrupted Biden and engaged in frequent arguments with the moderator, Chris Wallace of Fox News. Biden also was coarse, largely in response, calling Trump a “clown” and telling him to “shut up.” There was little discussion of substantive differences.

Polling that followed that initial meeting, which included the period during Trump’s treatment for covid-19, the disease caused by the coronavirus, generally showed Biden’s lead increasing slightly. Nationally, Biden has a 12-point lead in a Washington Post average of national polls, and seven- or eight-point leads in the crucial Great Lakes states of Pennsylvania, Michigan and Wisconsin, which flipped to Trump in 2016 to give him the presidency.

But political consultants in both parties do not consider the current advantage predictive of the election result. Trump eked out narrow wins in all three of those states after trailing by similar or slightly slimmer margins in public polling averages three weeks before the election. Those same polling averages, while not predicting Trump’s eventual victory, did show that he was able to close the gap in the final weeks.

The Trump campaign has been seeking another comeback in recent days, after allies helped arrange for the release of emails and photographs allegedly gleaned from the laptop of Biden’s son Hunter. The documents, initially published by the New York Post, suggest that Hunter Biden traded on his family’s name and may have introduced a business partner to his father, when he was vice president.

The Washington Post has been unable to verify the authenticity of the alleged emails or correspondence. Both Hunter Biden’s attorney and the Biden campaign denied that any meeting occurred.

The controversy around Biden’s son was not raised in either town hall.

“I know these are anxious times,” the elder Biden said at a fundraiser earlier in the day. “I appreciate everything you’re doing for the campaign. We have 19 days left, and you know, he’s going to throw everything but the kitchen sink at me.”

As the town halls opened, the coronavirus pandemic continued to rage across the United States, with 62,000 new cases reported Thursday, the highest level since late July. After infecting Trump, his wife and youngest son and several of his top advisers, there were signs the virus was not yet finished disrupting the campaign.

Sen. Kamala D. Harris (D-Calif.), Biden’s running mate, announced before the town halls that she had canceled travel plans until Monday after two people involved with the campaign tested positive for the coronavirus. Later Thursday, the Biden campaign announced it had learned that an administrative member of the company that charters Biden’s plane had also tested positive.

The Biden campaign said both candidates had not been in close contact with the infected people, though they had taken masked rides on airplanes with them. As a result, neither candidate currently plans to quarantine for the recommended 14 days after potential exposure to the virus.

Harris last tested negative for the virus Wednesday, their campaign said, while Biden was tested Thursday and no infection was detected.

Since leaving the hospital, Trump has resumed his near-daily mass rallies, heading often to states where the virus is rampaging to speak before thousands gathered in tight crowds and not wearing masks. Members of his family and other campaign surrogates have also been meeting with large crowds.

Biden and Harris have also begun regular travel, but they have intentionally avoided crowds, choosing other venues, including drive-in events where participants do not leave their vehicles and honk their approval.

As the candidates separately appeared before the nation Thursday, Biden received several questions about systemic racism and his involvement with the 1994 crime bill. Cedric Humphrey, a Black student from Harrisburg, Pa., told Biden that this election could be decided by Black voters under 30 who don’t vote, which he himself is contemplating.

“Besides ‘you ain’t Black,’ what do you have to say to young Black voters who see voting for you as further participation in a system that continually fails to protect them?” he asked, referring to a line Biden once used and apologized for.

Biden responded by quoting the late congressman John Lewis, who called voting a “sacred opportunity,” and then listed numerous proposals he has backed that would help Black Americans, including more funding for early education programs and historically Black colleges and universities, and start-up funds for Black entrepreneurs.

Biden said Trump deserves “a little but not a whole lot” of credit for his foreign policy, praising the recent deal with Israel but noting that North Korea continues to be a threat and China is “making moves.”

“We find ourselves in the position where we’re more isolated in the world than we’ve ever been,” he said. “ ‘America first’ has made America alone.”

Biden was asked what it will say about the country if he loses.

“Could say that I’m a lousy candidate, that I didn’t do a good job,” he answered. “But I hope that it doesn’t say that we are as racially, ethnically and religiously at odds with one another as it appears, as the president wants us to be.”

As his town hall progressed, Trump too fell into a rhythm, engaging with voter questions and charming one questioner who complimented his smile. He defended his recently released tax returns, calling the $750 he reportedly paid one year a “statutory” number.

“I am treated badly by the IRS, very very badly,” he said.

He said he did not owe Russia money, would work to provide solutions for young immigrants currently working in the country without permanent authorization and promised a cheaper health-care system with better products but did not say how he would do it — or why he hasn’t done it already.

He repeated the false claim that he is “always protecting people with preexisting conditions.” He currently supports a case in federal court that could throw out the Affordable Care Act and end those protections.

The final debate will take place Oct. 22, with plans for both candidates to meet in a direct debate format in Nashville, said Frank J. Fahrenkopf Jr. , the co-chairman of the debate commission.

That debate is expected to follow the same rules as the last meeting, with a roughly 12-foot distance between candidates and the audience required to wear masks. The Trump and Biden campaigns are scheduled to meet Friday to discuss final preparations and any other proposed precautions, Fahrenkopf said, and NBC News White House correspondent Kristen Welker, who will be the moderator, is expected to release a list of the six debate topics this week.