Let aequals=startset 9 comma 10 comma 11 comma 12 comma 13 comma 15 endset{9,10,11,12,13,15}.

a. how many subsets does a have?

b. how many proper subsets does a have?

Let A = {9,10,11,12,13,15}

in this set number of elements is equal to six.

we have to find how many subsets and proper subsets A have.

for finding number of subsets, we use the formula 2 raise to the power n, where n is the number of elements in the set A which is 6, it means 2⁶ subsets

so, set A have 2⁶ = 64 subsets

and to find the proper subsets use the formula 2ⁿ - 1 = 2⁶ - 1 = 64 - 1 = 63

so, set A have 63 proper subsets.