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The phrase "contrary to their" is correct and can be used in written English.
It generally implies that someone has done something in opposition to something else. For example, "The students performed well on the exam, contrary to their expectations."
Exact(60)
Contrary to their TV image, women's prisons aren't all bad.
But others considered such supplications contrary to their Christian beliefs.
Contrary to their expectations, the investigators found no increase in daytime drowsiness in healthy older people.
Yankee Stadium patrons graded on the curve yesterday, contrary to their notorious reputation.
Yet before the book is done, all four will take actions contrary to their natures.
Contrary to their repeated assertions, public spending is not out of control.
Contrary to their P.R. pitch, hedge funds aren't operating oblivious to market conditions.
"The actions of the Japanese government are completely contrary to their words.
Contrary to their exotic appearance, lotuses are not tender, tropical plants.
Contrary to their expectations, the results indicated that groups and individuals reached decisions equally quickly.
Contrary to their licentious reputation, most players can cope with the latter.
More suggestions(21)
contrary to their conscience
contrary to their duties
contrary to their excitement
contrary to their intent
opposition to their
contradiction to their
contradistinction to their
counter to their
inverse to their
averse to their
breaches to their
inimical to their
opposite to their
prejudicial to their
antithetical to their
in contrast to their
contradictory to their
opposed to their
incompatible with their
contrary to existing
contrary following the
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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