Tuesday was Justice Brett Kavanaugh’s first day as an associate justice of the U.S. Supreme Court — and his two daughters, Margaret and Liza, were planning on being there to watch their dad in action, as Kavanaugh noted during his ceremonial swearing-in Monday night at the White House.

About 20 protesters showed up before Kavanaugh’s first day, as NBC News reported; they chanted at the back of the building, near where the justices drive into the parking garage.

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The activists then moved briefly to the front of the building for a short time before eventually dispersing. Supreme Court police were prepared for far more activity than that — and for the possibility they might try to interrupt the court’s work.

Spectators in the court were warned that any outburst inside the building could be punishable as a federal offense, as several news outlets reported.

The Supreme Court heard two cases about the kind of crimes that can trigger long prison sentences, under a federal law intended to get repeat criminals off the streets.

Chief Justice John Roberts “offered the usual greeting for a new justice,” noted NBC News. Roberts wished Justice Kavanaugh “a long and happy career in our common calling.”

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Kavanaugh reportedly talked occasionally with Justice Elena Kagan; he sits beside her on the bench.

The incoming justice asked about a dozen questions during the argument of the two cases, said NBC News, both involving challenges to the way states interpret the Armed Career Criminal Act (ACCA). The ACCA is a federal law that provides sentence enhancements for felons who commit crimes with firearms if they are convicted of certain crimes three or more times.

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During the day’s first argument, about whether the state of Florida’s definition is so broad that it counts almost every purse snatching as a violent robbery, Justice Sonia Sotomayor asked if that state went too far in defining what actually counts as a violent robbery.

“Is a pinch, a[n] ordinary pinch — let’s not talk about an extraordinary — pulling of the ears that a parent might sometimes do … Let’s talk about just a pinch. Is that sufficient force?” she asked, as NBC News reported.

“At that point, she illustrated her point by pinching Justice Neil Gorsuch, at her right, to laughter in the courtroom,” said the news site.

Kavanaugh focused his questions on the court’s prior precedent, as the justices weighed “what level of force in a robbery is required” for the crime to be considered a violent felony under the ACCA, The Hill reported.

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He said the court’s ruling in a case known as Johnson v. United States requires “a substantial degree of force.”

“How are we supposed to deal with that language in the Curtis Johnson opinion if we’re trying to follow Curtis Johnson strictly?” Kavanaugh asked Frederick Liu, assistant to the solicitor general, who argued that a Florida man’s unarmed robbery should qualify as a violent felony.

Earlier Tuesday, the Supreme Court declined to review an environmental ruling written by Kavanaugh himself when he was an appeals court judge. The justices left in place Kavanaugh’s August 2017 opinion, which struck down an Obama-era Environmental Protection Agency rule, as NBC News noted.

Two other cases are to be argued this week, according to NBC News — one involving detention of illegal immigrants and another concerning liability for asbestos injuries in the U.S. Navy.

See more in the video below.