Hi Kooyeen: Your examples are not complete sentences. Maybe it's Ok to say these in casual conversation, but they are not correct. The one example that I can think of that is always correct is the imperative form, where the implied subject is "you".
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AlpheccaStars Maybe it's Ok to say these in casual conversation, but they are not correct.If something is ok to say in a particular context (register), it is correctin that context (register), by definition of a language.
Verb_aTIMTRYING TO FIX YOUR CAR AGAIN?To me, it is OK in casual conversation to say the above. However, strictly speaking, it is not grammatically correct.
KooyeenCan anyone give me some examples?do you, did you, have you, are you are often omitted in yes-no questions in the register you're interested in here -- as you illustrate with Trying to fix your car again?