Usually convince means "to cause (someone) to believe that something is true." Usually persuade means "to cause (someone) to do something by asking, arguing, or giving reasons." They can be used interchangeably but that is less common. Below are some examples of the most common uses of convince and persuade:
Even though the above examples are the most common uses, it's ok to use convince and persuade interchangeably, especially when you mean "to cause (someone) to do something by asking, arguing, or giving reasons."
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