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In my thesis I have the following sentence:
One can construct a new query by replacing all the variables in Q with their equivalence classes.
I doubt that this sentence is grammatically correct, for the following reason. Every variable is replaced by just one equivalence class, since there is only one equivalence class for every variable in Q. At the same time, there are multiple variables in Q. So should it be "equivalence class" or "equivalence classes"?
Use this instead:
One can construct a new query by replacing each variable in Q with its equivalence class.
Two previous answers suggested (as did Jim's answer too, but with equivalent instead of equivalence)
One can construct a new query by replacing each variable in Q with its equivalence class.
That rewording is acceptable, but note that you can fix your original sentence by adding the word respective:
One can construct a new query by replacing all the variables in Q with their respective equivalence classes.
Adding respective as shown indicates that each variable is replaced by its corresponding class.
It may be argued that the latter rewording is confusing, and the former is not. Certainly there are people who don't understand how respective works, which is a reasonable argument in favor of not using it when simple alternatives exist, as in the present case. A more important argument for discouraging use of respective is that numerous authors badly misuse it or overuse it; they may shorten their exposition by half a dozen words while tripling the difficulty of comprehending what they mean. But – just for the present case – I think it's to be recommended.
Your intuition that there's something wrong is correct, but what's wrong isn't the grammar, it's that the sentence doesn't mean what you want it to mean.
When you are describing an operation that occurs on individual things in a way that is specific to the individual ("every variable is replaced by just one equivalence class"), you want the word each, not all.
So the sentence that accurately describes your procedure is:
One can construct a new query by replacing each variable in Q with its equivalence class.
"Each" means that every variable is considered individually, and "its X" indicates that the replacement is with something that is particular to the variable.
When using "each", number agreement is going to be singular; when using "all", number agreement is plural.
