I know you can abbreviate the United States as U.S., US, or USA.
If you elect to use U.S., can you use a question mark after this version?
For example: Do you like to travel to the U.S.?
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Yes, when using an abbreviation that ends with a period, it is acceptable to follow this with another (different) punctuation mark, as in your example:
Do you like to travel to the U.S.?
Reference: Jack Lynch's Guide to Grammar and Style: