Question

PLEASE EXPLAIN: COLLEGE MATH


State the cardinality of the set.
The set of subsets of {1, 3, 7, 11, 13}

the answer is 32, but I don't understand how it got there.. I am taking an online college math course so there is no professor to help me and answer my questions so please bare with me..

Answer 1

Well, the set of all subsets is called the power set.
If a set has cardinality \(n\), then the power set will have cardinality \(2^n\).

Answer 2

In this case the cardinality is \(5\) so the powerset will have cardinality \(2^5=32\).

Answer 3

The reason why the cardinality of the power set is \(2^n\) is because we can think of each subset as having or not having any element in our original set. So for each element you put in the original set, the number of subsets it has will grow by \(2\).

Answer 4

oh ok thank you, the previous person told me that it was because of a combination formula. that has nothing to do with it right?

Answer 5

Ummm, well are you doing combinatorics right now?

Answer 6

You can certainly do the problem without knowing about the power set.

Answer 7

to be honest I am not sure

Answer 8

Never heard of Combo..

Answer 9

thank you so much!