Expert: Paul Klarreich - 2/4/2012

Question
*** I'm not asking you to solve this. Can you please explain how to do these types of problems? You can replace the numbers so its not the same. Please, I don't understand how to do these types of questions at all.

Given that set A has 47 elements and set B has 25 elements, determine each of the following:
Maximum and minimum number of elements in A U B

Maximum and minimum number of A intersection/upsidedown U with B.

Another question I'm having problems with:
A set has 8192 subsets. How many elements are in the set?

I'm so lost on how to do these problems. Please help me D:.

Answer
Questioner:Sarah
Country:Florida, United States
Category:Advanced Math
Private:Yes   <<<<<<<<<<<<<<<<<<<<<  changed
Subject:Sets, elements, subsets

Question:

*** I'm not asking you to solve this. Can you please explain how to do these
types of problems? You can replace the numbers so its not the same. Please,
I don't understand how to do these types of questions at all.
Given that set A has 47 elements and set B has 25 elements, determine each

of the following:
Maximum and minimum number of elements in A U B

.........................
Notation:  I use  A+B for union,  AB for intersection, A' for complement,
and n(A) for cardinality.  

If you don't know what those words mean, you are not ready to ask questions.

You should realize that if '+' is in between two NUMBERS, it's just
arithmetic.

Also:  A - B means  A(B') -- elements in A, but not B.  
........................

You normally do these with a 'Venn Diagram' (which you will look up)
and you will see that

n(A+B) = n(A) + n(B) - n(AB).

That says the cardinality of a union is the sum of the n's of the two sets

minus those elements that would get double-counted.  (Why would they be

double-counted?)

...........................................................

Maximum and minimum number of A intersection/upsidedown U with B.

You mean:  n(AB).

Start drawing Venn diagrams of two sets -- various possibilities.

Could there be NO things in the intersection?

Is it possible that all of B is in A?

Is it possible that all of A is in B?




Another question I'm having problems with:
A set has 8192 subsets. How many elements are in the set?

Don't you have some rule that says:

If A has x elements, then A has .... subsets.

See how that rule relates to the number 512, ot 256, or 8192.  Why did I

pick those numbers?