Question

Let A  {1, 2, 3, 4} and B  {x, y, z}. (a) List five functions
fromAtoB. (b)Howmany functions f : A→B are there?
(c) How many functions f : A→B are one-to-one? (d) How
many functions g: B →A are there? (e) How many functions
g: B →A are one-to-one? (f) How many functions f : A→B
satisfy f (1)  x? (g) How many functions f : A→B satisfy
f (1)  f (2)  x? (h) How many functions f : A→B satisfy
f (1)  x and f (2)  y?

Answer 1

Here is what I got for my answers
a) (1) {(1, x), (2, x), (3, x), (4, x)} (2) {(1, y), (2, y), (3, y), (4, y)}
(3) {(1, z), (2, z), (3, z), (4, z)} (4) {(1, x), (2, y), (3, x), (4, y)}
(5) {(1, x), (2, y), (3, z), (4, x)}
b) 34 c) 0 d) 43 e) 24 f ) 33 g) 32 h) 32

Answer 2

Lets A = {1,2....k} and B = {1,2....n} then:
f : A→B = n^k
f : A→A = k^k
f : B→A = k^n
f : B→B = n^n

f : A→A = k!, for one to one
its the same for any set

Answer 3

hope it will help you a little

Answer 4

I forgot this f : B→A one to one:
n*(n-1)...(n-(k-1)) if k<n,
n! or k! if k=n, and for k>n result = 0