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The phrase "a set that is" is correct and usable in written English.
It can be used when describing a specific collection of items or elements that possess certain characteristics or properties.
Example: "We are studying a set that is defined by its unique properties in mathematics."
Alternatives: "a collection that is" or "a group that is".
Exact(44)
The result is a set that is often easier to admire than enjoy.
This set allows so much more to be written and said than is possible in a set that is created as a whole.
"THE UGLY DUCKLING," a musical version of the Hans Christian Andersen story, is performed against a set that is a reproduction of one of Monet's "Water Lilies" paintings.
In Lady Rizo: Multiplied at Assembly Checkpoint, the American singer with a line in cheeky self-revealing patter offers up a set that is one great love song.
"THE UGLY DUCKLING," a musical version of the Hans Christian Andersen story, performed against a set that is a reproduction of one of Monet's "Water Lilies" paintings.
Though it has been 18 years since the award-winning DJ's last dance with comedy, he has produced a set that is up to date on the current idioms and segues.
Similar(16)
It was a tender, exposed moment in a set that was defiant but difficult to love.
At another point, they constructed a set that was meant to look like a Saddam Hussein-era military base.
On Thursday night he played a set that was deferential but un-self-conscious, at ease in its evocation.
The context helped make sense of a set that was often disjointed, with some promise but ample room for improvement.
A set that's matured beautifully in the years since its original release.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com