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Sentences conveying confident intentions produced by Chinese speakers are
unlikely ________ the attitudes of friendly or hostile.

1.show 2. to show 3. showing

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I agree with Jason. 'to show' would be correct.

However, just to add, I would change the sentence structure at the end. It sounds a bit quirky.

Sentences conveying confident intentions produced by Chinese speakers are unlikely to show friendly or hostile attitudes.

Your sentence is technically correct but sometimes uneccesarry prepositions make a sentence longer than needed.

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...unlikely to show the attitudes of friendly or hostile.

The phrase to show is called the infinitive.

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