3. Let X be a set and let AX. (i) Define a function A:X{0,1} by the rule A(x)={10ifxAifx/A. The function A is called the characteristic function of A. Show that 1(0)=X\A and that 1(1)=A. When is A a constant function? For which sets X and subsets A is A injective? Surjective? A bijection? (ii) Suppose that f:X{0,1} is any function. We have defined the subset f1(1) of X : f1(1)={xX:f(x)=1}. Show that f is the characteristic function of f1(1), i.e. that f1(1)=f. (Note: (i) and (ii) show that there is a bijection from P(X) to {0,1}X. In particular, if X is finite and #(X)=n, then #(P(X))=2n.)