Answer:
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