The full faith and credit clause of the U.S. Constitution requires states to recognize and honor the public acts, records, and judicial proceedings of other states. This generally means that certain legal decisions or documents (such as marriage licenses, driver's licenses, and court judgments) are valid across state lines.
Among the options you provided, citizens can legally drive a car in one state with a driver's license from another state due to the full faith and credit clause, as states generally recognize valid driver's licenses issued by other states.
The other options do not relate to the full faith and credit clause:
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Paying income taxes for a state where you don’t live if their taxes are lower is more about tax laws than about the full faith and credit clause. People typically pay taxes based on their residence.
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Refusing to serve people in a business based on personal beliefs is an issue of state and federal anti-discrimination laws, not the full faith and credit clause.
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Telling lies about a political leader falls under free speech and defamation laws, rather than the full faith and credit clause.
So, the correct answer to your question is: Drive a car in one state with a driver's license from another state.