What their plans represent, Mr. Levitt said, “is an emerging consensus among Democrats of what a health care reform plan might look like in 2021 other than Medicare for all, if the party wins in 2020.”

What the Facts Are:

Mr. Sanders and Mr. Biden both charged that a Bloomberg policy in New York City went after African-American and Latino people.

What MR. Sanders Said:

“Mr. Bloomberg had policies in New York City of stop and frisk, which went after African-American and Latino people in an outrageous way.”

This is true. A judge ruled in 2013 that the tactics underlying stop and frisk as practiced in New York disproportionately stopped blacks and Latinos.

What MR. Biden Said:

“He had stop and frisk, throwing close to five million young black men up against a wall.”

He later added: “The reason that stop and frisk changed is because Barack Obama sent moderators to see what was going on. When we sent them there to say this practice has to stop, the mayor thought it was a terrible idea we send them there, a terrible idea.”

This is mostly false. New York’s wholesale stop-and-frisk policy began its death spiral with a report in May 2012 from the New York Civil Liberties Union that revealed more than 685,000 stops had been made the year before. The next month, Mr. Bloomberg announced that the program was going to be overhauled, and over the next year, the number of stops plummeted. Lawsuits were also underway or about to be filed. In August 2013, as Mr. Bloomberg approached his final months in office, a judge ruled against the city and as part of the remedies, appointed a monitor. Mr. Bloomberg strongly objected to the monitor, to no avail. By then, the number of monthly stops had declined by more than 90 percent from its peak.

What the Facts Are:

Mr. Bloomberg accurately cited his record on coal plant closings.

What He Said:

“Well, already we’ve closed 304 out of the 530 coal-fired power plants in the United States.”

This is true. Mr. Bloomberg was referring to his more than $100 million contribution to the Sierra Club’s Beyond Coal campaign since 2011. According to the Sierra Club, 304 coal-fired power plants have since either retired or have announced plans to close. They estimate that 40 percent of those closings would have not happened had it not been for the campaign. Over all, he has donated about $278.2 million to environmental and climate change causes, according to a recent tally by The New York Times, and as a mayor of New York City, had a strong record on climate change.

What the facts are:

Mr. Biden and Mr. Buttigieg misrepresented the possibility that their proposals could raises taxes on small businesses.

What they said:

Asked if their plans would raise taxes on small businesses,

Mr. Biden said, “No, taxes on small businesses won’t go up.”