Question

how many choice function define on the set X

X = {{0,1},{2,3},{4,5}}

Answer 1

A function that chooses one element out of each non-empty subset of a set A is called a choice function for A.

The choice function simultaneously chooses an element from each of many sets.

Thus, from every subset of X we have to choose 1 element out of 2 (as each subset consists of 2 elements each).

Any choice function will choose one of these 2 possibilities for each of the 3 subsets of X.

Thus number of choice functions $=C(2,1)*C(2,1)*C(2,1)$

$=8$

where, $C(n,m)= n!/[(m!)*((n-m)!)]$