Daily bombardments of false claims and false equivalences have forced reporters to challenge the president in real time — and sometimes, to his face.

CBS News correspondent Paula Reid did just that Monday when Trump talked to reporters on his way from the Oval Office to Marine One. The president repeated a false claim that he and the Obama administration had the same policy of separating migrant children from their parents.

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“Obama had a separation policy; we all had the same policy,” Trump said, answering a question from Reid — who corrected him on the spot.

Reid: You did not —

Trump: I tried to do it differently, but Obama had a separation policy.

Reid: Sir ―

Trump: But people don’t like to talk about that.

Reid: Sir, it was different. You decided to prosecute everyone at the border.

The president ignored Reid’s follow-up comments, but she was praised for pointing out to the president that what he said was wrong.

“Kudos to CBS correspondent Paula Reid,” CNN chief media correspondent Brian Stelter wrote in his daily newsletter.

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Reid’s question was prompted by a presidential tweet a day earlier.

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Trump on Sunday attacked “60 Minutes” for airing what he called a “phony story” about the family separation crisis and claimed that the policy did not start with his administration. Barack Obama and George W. Bush both separated migrant children from their parents “because that is the policy and law,” he tweeted.

That claim is false and was debunked by The Post’s Fact Checker in June and again on Tuesday. The Justice Department under former attorney general Jeff Sessions rolled out a “zero tolerance” policy of apprehending and prosecuting adults who were caught crossing the border illegally. Thousands of children, who can’t be detained or prosecuted, were separated from their parents.

“This is worlds apart from the Obama- and Bush-era policy of separating children from adults at the border only in limited circumstances, such as when officials suspected human trafficking or another kind of danger to the child, or when false claims of parentage were made,” The Post’s Salvador Rizzo wrote.

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And as The Post reported in June, the idea of ramping up prosecutions of adults who enter the country illegally was conceived during the migrant crisis of 2014. But officials in the Obama administration and the Department of Homeland Security considered the policy too extreme. The Trump administration was willing to try it.

CBS News declined an interview request for Reid. A spokeswoman said the reporter’s questions and follow-up comments spoke for themselves.

Reporters and media organizations have found ways to fact-check the president’s daily streams of usually repetitive falsehoods. The Post’s Fact Checker, for example, has a searchable database of false or misleading claims Trump has made since assuming office: 6,420 as of Oct. 30 ― about 10 a day. The database can be filtered by topic, and shows which false claims Trump has repeated the most and when he repeated them.

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Fact-checking Trump is not hard because he “tells the same lies over and over,” Dale, the Toronto Star Washington bureau chief, wrote in a column published by The Post, citing as an example the baseless and often-repeated claims of widespread voter fraud.

“Listen to this president long enough, and you can almost sense when a lie is coming. If Trump tells a story in which an unnamed person calls him ‘sir,’ it’s probably invented. If Trump claims he has set a record, he probably hasn’t. If Trump cites any number at all, the real number is usually smaller,” Dale wrote.

Dale also has created a database of the president’s false claims, filtered by topic and by source. He has noted 3,800 false claims since Trump took office. (The Post’s database is more robust because it includes misleading claims in addition to false ones.)

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Fact-checking Trump on live television can be more difficult. As The Post’s Erik Wemple wrote, rebutting falsehoods as they’re uttered wouldn’t keep the attention of a live audience, especially when rapid-fire misstatements are blurted out at campaign rallies.

“Morning Joe” co-host Joe Scarborough tried to do so during Trump’s NATO news conference in July. During the show, Scarborough listened to Trump and interrupted every time the president said something false. The show aired the news conference and Scarborough’s real-time fact check side by side.

And reporters who interview Trump during news conferences or in gaggles, as Reid did outside the White House on Monday, may find themselves in a verbal showdown with the president. Just ask CNN chief White House correspondent Jim Acosta, whose White House press pass was suspended (and later restored) after he engaged in a testy exchange with Trump.

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“It’s not just me; a lot of us do this — [we] push back on these falsehoods on a daily basis,” Acosta said in August on “The Late Show With Stephen Colbert.”