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The phrase "relation exists" is correctly constructed and can be used in written English.
You can use it when referring to the fact that something has a connection to another thing, or that something has some kind of relationship to something else. For example, "The relation between cause and effect exists in all aspects of life."
Exact(60)
In general, however, one should not simply assume without argument that an uninstantiated property or relation exists.
During the early 20th century, pharmacologists became aware that a relation exists between the chemical structure of a compound and the effects it produces in the body.
Where the paired relation exists, however, continual elongation of one or both may eventually result in a junction and the formation of a column.
What relation exists between FEs and geomagnetic storms?
What relation exists between these two ways of structuring space?
The inverse relation exists for commercial customers (see Fig. 5b).
Davidson happily concedes that no such relation exists between mental and physical properties and events.
A direct relation exists between saturation of the reaction atmosphere and the kinetics of carbothermal reduction.
The present study was designed to address whether such a relation exists after DES placement.
Results show that a complex relation exists between PCM and TCE volume percentages.
A power-law relation exists between the convection flow rate and the dimensionless vibration velocity.
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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