“Thus” and “so”
The most important difference between “thus” and “so” is that “so” is a conjunction (meaning “and for that reason”, “and because of that”), whereas “thus” is an adverb (synonymous with “consequently”) and cannot join two independent clauses. For example, the sentence:
He is not satisfied, so we must prepare a new proposal.
can be rewritten using “thus” as follows:
-He is not satisfied. Thus, we must prepare a new proposal.
-He is not satisfied; thus, we must prepare a new proposal.
-He is not satisfied, and(,) thus(,) we must prepare a new proposal.
“Thus” is usually separated from the rest of the sentence by commas, but the commas are often omitted if this would lead to three commas in a row (as in the third example).
***“Thus” also has another meaning: “in this way”, “like this” (in which case it does not introduce a clause). For example:
They have developed a new technology, thus allowing them to reduce costs.
The comma here was appropriate because what follows “thus” is not a clause. It is just a parenthetical expression extending the preceding clause.
“Hence”
Just like “thus”, “hence” is an adverb, not a conjunction, so it cannot join two independent clauses (note that it is more common to omit the commas around “hence” than
-He is not satisfied. Hence(,) we must prepare a new proposal.
-He is not satisfied; hence(,) we must prepare a new proposal.
“Hence” used in this sense is rather uncommon, and such usage persists mostly in specialized fields, such as scientific writing.
There is, however, another, more common meaning of “hence”, which substitutes a verb but is not a clause in itself and is always separated from the rest of the sentence by a comma:
Our server was down, hence the delay in responding.
The chemicals cause the rain to become acidic, hence the term “acid rain”.
As you can see, “hence” substitutes phrases such as “which leads to” or “which is the reason of”.
“Therefore”
Finally, “therefore” is also an adverb meaning “as a logical consequence”. It is used mostly in argumentation when one statement logically follows from another, and it is common in scientific literature.
Again, style guides usually recommend to set it off with commas, but when this would break the natural flow of the sentence, most authors tend to omit the commas:
-The two lines intersect. Therefore(,) they are not parallel.
-The two lines intersect; therefore(,) they are not parallel.
-The two lines intersect, and(,) therefore(,) they are not parallel.
Note that “therefore” does not sound natural when there is no apparent logical connection between the two statements, especially in an informal context. You should use “so” in such cases:
The trip was cancelled, so I visited my grandma instead.
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