Let X be the nonempty set and let A be a subset of X. We illustrate the characteristic function x_A ?X?{0, 1} of the set A by x_A (x)= {(1 if x?A 0 if x?A)
a.) Since this is called the characteristic function, it probably is a function, but check this carefully anyway.
b.) Determine the domain and range of this function. Make sure you look at all possibilities for A and X.