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..

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..

asnaseer · Answer

The set of all sub sets will give you a set with the empty set in it plus all ways of creating a sub set of {1, 3, 7, 11, 13}

asnaseer · Answer

since the set given to you has 5 elements in it, this results in:

1 + C(5,5) + C(5,4) + C(5,3) + C(5,2) + C(5,1)

i.e. empty set + number of ways of picking 5 items from 5 + number of ways of picking 4 items from 5 + ...

anonymous · Answer

ok and how do you get 32?

asnaseer · Answer

Work out the combinations and you should get 32

asnaseer · Answer

$$C(n,r)=\frac{n!}{r!(n-r)!}$$

anonymous · Answer

what number fits n and r?

asnaseer · Answer

1 + C(5,5) + C(5,4) + C(5,3) + C(5,2) + C(5,1)

anonymous · Answer

I looked in my text book and that equation is not in there this is for Cardinality and Sets.

asnaseer · Answer

Did you follow the reasoning above?

anonymous · Answer

yes i still dont get it

asnaseer · Answer

Do you know what cardinality of a set means?

anonymous · Answer

yes the number of elements in a set

asnaseer · Answer

ok, so now do you know how to work out the number of sub sets of a set of 5 items?

anonymous · Answer

no

asnaseer · Answer

that is what I tried to explain above. so you did not follow the reasoning then?

asnaseer · Answer

lets start from a simple set. lets say we have a set with just one element in it {a}
how many sub sets can you create from this?

anonymous · Answer

im not sure is it infinite?

asnaseer · Answer

How can a set of just one member have an infinite number of sub sets?

anonymous · Answer

im not sure that is why i am asking im so confused.. i am taking this course online so there is no professor to be there to explain.. it is an online course with only a textbook..

anonymous · Answer

I am basically trying to teach myself the questions..

asnaseer · Answer

It /seems/ then that you are tackling a problem before understanding the basic principles of set theory. I would suggest you first revise up on the fundamentals of set theory and then come back to this question. Otherwise you will only get more confused.