Suppose that a a is a set containing 13 13 elements. find the number of different subsets of a.

number of subsets of a set with 13 elements are:

Step-by-step explanation:

In order to solve this intuitively, we can start by a set with lesser elements. This will reveal a pattern that will be used to solve for the subsets of the 13 element set.

If we start with a set B. which contains only 3 elements.

how many subsets of B are there? well we can count them. [the set containing {1,2} and {2,1} are the same, arrangement doesn't matter]

there are a total of 9 subsets here.

Similarly, if you try a with a subset with only two elements you'll find that it has a total of 4 subsets.

We can see that combinatorics is at play here.

for the set B. the number of subsets can be written as:

if we try with a 2-element set:

We can use the same technique to find the number of subsets of the 13 element set.

But if you recognize a pattern here that this sets of combinations are actually part of the pascal triangle, the sum of each row of the triangle is 2^{the row's number}. hence.

So finally, the subsets of a 13-element set A will be

answer: 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

step-by-step explanation:

765238725478629038640962136509762139056074

step-by-step explanation:

64087235609746097215074621039754021037