1. I am sure that he will succeed.

2. I'm not sure that he will succeed.
3. I'm not sure if he will succeed.
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Are all grammatical? is 'that he...' a noun phrase or an adverbial phrase?

Is 'if he will...' a noun phrase or an adverbial phrase?

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4. I am sure (of) that he will succeed.
5. I'm not sure (of) that he will succeed.
6. I'm not sure (of) if he will succeed.

In each sentence, is 'the preposition 'of' missing?

Yes, all of the sentences are grammatically correct. The phrase "that he will succeed" is an adverbial phrase, and the phrase "if he will succeed" is a noun phrase. In sentences 4, 5, and 6, the preposition "of" is optional and can be included or omitted.

1. I am sure that he will succeed. - Yes, this sentence is grammatical. "That he will succeed" functions as a noun clause serving as the direct object of the verb "am sure."

2. I'm not sure that he will succeed. - Yes, this sentence is grammatical as well. "That he will succeed" functions as a noun clause serving as the direct object of the verb "am sure."

3. I'm not sure if he will succeed. - Yes, this sentence is grammatical too. "If he will succeed" functions as a noun clause serving as the direct object of the verb "am sure."

In each of these sentences, "that he will succeed" or "if he will succeed" is a noun clause functioning as the direct object of the verb "am sure."

Now, let's move on to the next set of sentences:

4. I am sure (of) that he will succeed. - Yes, this sentence is grammatical. The preposition "of" is optional in this context.

5. I'm not sure (of) that he will succeed. - Yes, this sentence is also grammatical. The preposition "of" is again optional.

6. I'm not sure (of) if he will succeed. - Yes, this sentence is grammatical as well. The preposition "of" is optional here.

In all these sentences, the preposition "of" is optional and can be included or omitted based on personal preference.

1. I am sure that he will succeed. - This sentence is grammatically correct. "That he will succeed" is a subordinate clause acting as the object of the verb "sure."

2. I'm not sure that he will succeed. - This sentence is grammatically correct. "That he will succeed" is a subordinate clause acting as the object of the verb "sure."

3. I'm not sure if he will succeed. - This sentence is grammatically correct. "If he will succeed" is a subordinate clause acting as the object of the verb "sure."

In all three sentences, "that he will succeed" and "if he will succeed" are noun clauses functioning as the direct objects of the verb "sure."

Regarding the usage of the preposition "of":

4. I am sure (of) that he will succeed. - The preposition "of" is not necessary in this sentence. The sentence is grammatically correct without it. However, you can include "of" before "that" to add emphasis or clarify the object of certainty.

5. I'm not sure (of) that he will succeed. - Similar to the previous sentence, the preposition "of" is not required here. It is optional and does not affect the grammaticality of the sentence.

6. I'm not sure (of) if he will succeed. - Again, the preposition "of" is not needed in this sentence. It is optional and does not change the meaning or grammar of the sentence.

1. "I am sure that he will succeed." - This sentence is grammatical. In this sentence, "that he will succeed" is a noun clause acting as the direct object of the verb "sure."

2. "I'm not sure that he will succeed." - This sentence is also grammatical. Here, "that he will succeed" is again a noun clause, functioning as the direct object of the verb "sure."

3. "I'm not sure if he will succeed." - This sentence is grammatical as well. In this case, "if he will succeed" is a conditional clause functioning as the direct object of the verb "sure."

In sentences 1, 2, and 3, "that he will succeed" and "if he will succeed" are both noun clauses acting as direct objects. They provide the content of what the speaker is sure about or unsure about.

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4. "I am sure (of) that he will succeed." - This sentence is grammatical. In this sentence, "of" is optional. It can be used to indicate the object of the certainty.

5. "I'm not sure (of) that he will succeed." - This sentence is also grammatical. And similarly, "of" is optional and can be used to indicate the object of the uncertainty.

6. "I'm not sure (of) if he will succeed." - This sentence is grammatical as well. Once again, "of" is optional and can be used to indicate the object of the uncertainty.

So, in sentences 4, 5, and 6, the preposition "of" is optional. It can be included, but it can also be omitted without changing the meaning of the sentences.