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

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol

jeff jeff

step-by-step explanation: