Hello, I\'ve spent over an hour on this problem. Cansomeone please help? Find al

Question

Hello, I've spent over an hour on this problem. Cansomeone please help? Find all possible functions f: A --> B in eachcase below. Describe the functions by listing their orderedpairs.
a) A = {1,2,3} and B = {5} b) A = {4} and B = {5,6} c) A = {1,2} and B = {5,6} The problem ends here. The answers below is what I came up with: a) {(1,5),(2,5),(3,5)} b) {(4,5),(4,6)} c) {(1,5),(1,6),(2,5),(2,6)} Hello, I've spent over an hour on this problem. Cansomeone please help? Find all possible functions f: A --> B in eachcase below. Describe the functions by listing their orderedpairs.
a) A = {1,2,3} and B = {5} b) A = {4} and B = {5,6} c) A = {1,2} and B = {5,6} The problem ends here. The answers below is what I came up with: a) {(1,5),(2,5),(3,5)} b) {(4,5),(4,6)} c) {(1,5),(1,6),(2,5),(2,6)}

Explanation / Answer

A function with domain A to codomain B is by definition asubset of A x B such that no two first coordinates are the same andevery element in A occurs as a first coordinate. (Note: Thisdefinition that I'm using automatically excludes the empty set as afunction).
b) A function cannot have repeating first coordinates.Therefore the only functions from {4} to {5, 6} are:
func 1: {(4, 5)} func 2: {(4, 6)}
c) Here, each element in A can map to 2 different things.Hence, you will have 4 different functions.
func 1: {(1, 5), (2, 5)} func 2: {(1, 5), (2, 6)} func 3: {(1, 6), (2, 5)} func 4: {(1, 6), (2, 6)}
In general, if A and B are finite sets and n is the size of Aand m is the size of B. Then you will have m^n possiblefunctions.

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