The example that I can think of is a deck of playing cards. The two events that don't have a common set would be the black card and the red card. They are mutually exclusive because there can only be two possible colors. If the card is not red, then it is black (and vice versa). There is no card that consists of both colors.
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
