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Rudy Giuliani has been bragging to pals about having an affair with a married woman with “big boobs,” sources tell The Post.

The former mayor didn’t reveal the ample-bosomed woman’s identity, the sources said — but rumored mistress Maria Ryan matches that description on both fronts.

Giuliani on Wednesday called the claims “totally false,” saying “whoever told you that is a liar.”

But a day earlier, the 74-year-old member of President Trump’s personal legal team also denied cheating on wife Judith Nathan with Ryan, a married, 53-year-old New Hampshire hospital administrator, before Nathan filed for divorce in April.

But Nathan, his soon-to-be-ex, told The Post that Rudy’s assertion was a lie, saying, “My husband’s denial of the affair with the married Mrs. Ryan is as false as his claim that we were separated when he took up with her.”

Giuliani and Ryan were spotted sharing an intimate evening at a ­resort hotel in Whitefield, New Hampshire — two hours from Ryan’s home in Manchester — five days before Nathan’s April 4 divorce filing.

That day, he had toured the 25-bed Cottage Hospital she runs in the town of Woodsville, telling TV reporters he was there to learn about its cybersecurity system.

But later, the pair headed to the four-star Mountain View Grand Resort and Spa in Whitefield, where Giuliani had booked a luxury suite, according to sources.

The lovebirds dined with three male guests in the resort’s private dining area — and later watched “The Godfather” and “Godfather II” in a private screening room.

Giuliani insists they’re only friends, saying “I never spent the night with her” — but then adding he was “in effect separated’’ from Nathan at the time.

It was hardly their only meeting.

He was back in Manchester over the Memorial Day weekend to preside over Ryan’s nephew’s wedding, Giuliani told The Post on Tuesday.

Indeed, he flew to Fort Lauderdale, Fla. that same month to defend Ryan’s daughter, Vanessa, in court against charges of car-insurance fraud.

Giuliani told the Daily Mail at the time that the 32-year-old is personal assistant — although she is not listed on the employee roster for his security firm, and her LinkedIn profile says she works for JetBlue.

And just last week, he and Ryan were in Israel together, visiting the Hadassah Medical Organization in Jerusalem. In a press release about the visit, the hospital described Ryan as Giuliani’s “partner.”

Nathan was Giuliani’s third wife. He first married one of his second cousin, and then Donna Hanover — who divorced him in 2002 amid accusations that he was cheating with Nathan.

A person familiar with Giuliani called The Post to say the “big boobs” comment didn’t sound like him.

“That is not the way he talks about women, not the way he talks about people he does business with,” said the source.

Ryan was nowhere to be seen at her Manchester home Wednesday, where her husband calmly told a Post reporter to, “F–k off.”

“Get out of here. I already made a statement. We’re done here,” said former Marine Bob Ryan as he smoked a cigar on the porch next to his dog.

Additional reporting by Stephanie Pagones