Answer:

Cardinality refers to the number of elements in a finite set and Power set of A or  P(A)  refers to the set that contains all the subsets of  A . Hence, cardinality of  P(A) refers to the number of subsets of  A .

Here,  A=0,1,2,3,4,5,6,7,8,9,10  

|A|  i.e. cardinality of A is  11 .

If  A  is a finite set with  |A|=n  elements, then the number of subsets of A is =2n.  

Again,  |P(A)|  = number of subsets of  A=2n  

Putting  n=11 , we get that |P(A)|  is  211 .