For each of the functions below, indicate whether the function
is onto, one-to-one, neither or both. If the function is not onto
or not one-to-one, give an example showing why.
(1 )f: {0, 1}4?{0, 1}3. The output of f is
obtained by taking the input string and dropping the first bit. For
example f(1011) = 011.
(2) Let A be defined to be the set {1, 2, 3, 4, 5, 6, 7,
8}. f: P(A) ? {0, 1, 2, 3, 4, 5, 6, 7, 8}. For X ?
A, f(X) = |X|. Recall that for a finite set A, P(A)
denotes the power set of A which is the set of all subsets of
A.
(3)A = {a, b, c}, h: P(A) ? P(A). For X ? A, h(X) = X ? {a}.