Question

how many choice function we could we define on the set X
X= {{0,1},{2,3},{4,5}}

Answer 1

The Cartesian products of n sets $X_1, X_2, ..., X_n$ is the set of ordered n-tuples,

$X_1\times X_2\times ...\times X_n=\{(x_1,x_2,...,x_n):x_i\in X_i\ for\ i=1, 2, ...n\},$

where $(x_1,x_2,...,x_n)=(y_1,y_2,...,y_n)$ if and only if $x_i=y_i$ for every $i=1,2,...,n.$

The function that assigns 0 to the set {0,1}, 2 to {2,3}, and 4 to {4,5} is a choice function on X.

The function that assigns 0 to the set {0,1}, 2 to {2,3}, and 5 to {4,5} is a choice function on X.

The function that assigns 0 to the set {0,1}, 3 to {2,3}, and 4 to {4,5} is a choice function on X.

The function that assigns 0 to the set {0,1}, 3 to {2,3}, and 5 to {4,5} is a choice function on X.

The function that assigns 1 to the set {0,1}, 2 to {2,3}, and 4 to {4,5} is a choice function on X.

The function that assigns 1 to the set {0,1}, 2 to {2,3}, and 5 to {4,5} is a choice function on X.

The function that assigns 1 to the set {0,1}, 3 to {2,3}, and 4 to {4,5} is a choice function on X.

The function that assigns 1 to the set {0,1}, 3 to {2,3}, and 5 to {4,5} is a choice function on X.

We could define $2\times2\times2=8$ choice functions on the set X.