- This fog is so thick, you can cut it with a knife.
- This fog is so thick that you can cut it with a knife.
Also, if only one is a dependent clause, please explain why.
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The first example contains two clause that are fully independent and could be separate sentences.
This fog is so thick. You can cut it with a knife.
Many people would see the close connection between the sentences, and punctuate with a semicolon:
This fog is so thick; you can cut it with a knife.
The function of the second clause must be inferred from its meaning.
(Use of a comma would result in a "run-on sentence". These are sometimes considered errors in written English, but are quite common "errors" that native speakers often make.)
In the second case, there is a subordinating conjunction: "that". This introduces a subordinate clause. The meaning is the same, but the two clauses are linked by the word "that" which tells us the function of the second clause is to give a reason for the first. So the second clause is subordinate in the second example. Its function is implied by the word "that" rather than being inferred from the meaning of the clauses.
Subordinate clauses are also called dependent clauses.