a. Let A = {1, 2, 3, 4, 5, 6, 7} and B = {v, w, x, y, z}. Determine the number of functions /: A → B where
(i) f(A) = {v, x};
(ii) |f(A)| = 2;
(iii) f(A) = {w, x, y};
(iv) If(A) | = 3;
(v) f(A) = {u, x, y, z}; and
(vi) |f(A)| = 4.
b) Let A, B be sets with | A| = m > n = |B|. If k ∈ Z+ with 1 < k < n, how many functions f: A → B are such that |f(A)| = k?