Which one is correct:
"Do you think that this is correct?" or "Do you think if this is correct (or not)?"
"Do you know that he is coming?" or "Do you know whether he is coming?"
'Do you think if...' would only work in a context such as 'Do you think, if this is correct, I could print it out now?' You could simply say 'Do you think this is correct?
'Do you know whether he is coming?' would be the usual version. Supposing that you were very doubtful of the other person's statement, you might ask them 'Do you know that he is coming (because I think it unlikely)?'
Which one is correct "Do you think that this is correct?" or "Do you think if this is correct (or not)?" ?
A. They are both correct.
Find out why, read below.
After reading, apply same thing to "that" vs. "whether."
"Whether" functions exactly like "if"
Discussion: Examine the separate functions "that" and "if" have in a sentence. Let's do that below:
"Do" simply makes sentences interrogative (into a question.) For this exercise, drop the do.
That: Adjective clause (LBH P. 252/University of Pittsburgh "adjective clauses" web. https://www.pitt.edu/~atteberr/comp/0150/grammar/adjclauses.html
One of five that introduce an adjective clause (Who, Whom, Whose, Which, and That)
Why is this important? Do the exercise on your sentence. Put the do back in.
"Do you think that..." is the adjective clause. Adjective clauses are subordinate clauses.
The subject of a sentence is always the most important part of a sentence (it's the subject!) Whatever the adjective clause creates is the important part as it modifies the noun/subject (in this case modifies the subject to what the subject thinks.)
Example: Do you think that Sharon cooks chicken?
"if" - is a common subordinating conjunction. Provides "condition."
A subordinating conjunction like "if" connect independent clauses to a dependent clause. (https://grammar.yourdictionary.com). Adding "if" - to the head of the clause makes the clause subordinate and dependent on a main clause.
A dependent clause adds extra information to the main clause. Dependent clauses cannot stand by themselves and their meaning is dependent on the independent clause.
With this, Ask yourself - where's the subject, verb, object in these two sentences using "if." Do that by asking which is the main clause. Which is the dependent clause that adds extra information?
If you leave me, I'm going to take the bus home.
Do you think if this this car works(or not)?
Karen will think I'm funny, if I go home.
If I think money grows on trees, people will think I'm crazy.
What you arrive at is both these sentences you provided the subject, verb, and object are the same (Do you think). It's just that "that" and "if" are separate with completely different functions in the sentence.
if provides a condition and creates the subordinate clause.
"that" has no condition. It simply functions to strongly bind modifiers to a subject in a sentence. The first sentence is stronger; more definitive. Someone stating "Do you think that this is correct?" Makes the speaker sound stronger and more sure.
"if" since it is a subordinating conjunction, adds condition. It can have the effect of making the speaker's statements or questions sound weaker. Make the speaker appear less sure of themselves, especially when asking someone what they think about something.
Most will point you to choose the first sentence. It is more direct when asking a question. "Whether' functions in a sentence exactly like "if," as whether is a subordinating conjunction that adds condition.