# Cardinalities and ultimate sets

Show 40 post(s) from this thread on one page
Page 2 of 2 First 12
• Nov 29th 2011, 05:16 PM
ehpoc
Re: Cardinalities and ultimate sets
The prof says there is no typo.

I am going to go down to his office tomorrow. I will be sure to let you know what is going on here.
• Nov 29th 2011, 09:12 PM
Annatala
Re: Cardinalities and ultimate sets
Thanks, let us know. Something's definitely fishy...

Oh, and while you're at it, ask him what a positive set and an ultimate set are, since I still have no clue what those mean. (And where did he get those terms...?)
• Nov 30th 2011, 03:50 PM
ehpoc
Re: Cardinalities and ultimate sets
Well first off ultimate sets are all of the possible combinations of all intersections of the sets. I am sure that doesn't make sense.

But say you have set A and set B and A intersects B.

The ultimate sets would be the intersections

AB^c

A^cB

A^cB^c

AB

Basically it is all of the smallest possibly sets, or all the sets that have no subsets in them.

so for three sets A B C it would be the intersections....

A^cBC
AB^cC
ABC^c
A^cB^cC
A^cBC^c
AB^cC^c
A^cB^cC^c
ABC

So anyways on to this question. Which in all honesty was just a HORRIBLE question, and one could argue the epitome of what a trick question is. The prof actually went over it quickly at the beginning of class because "lots of people were confused by it". Ya no doubt genius it is completely horrible and a trick question.

Quote:

3. In a sample of 1000 cottage owners, 570 owned their cottages with no mortgage and
also owned cars; 340 owned mortgaged cottages, owned cars, and had electricity; 189
had neither mortgages nor cars nor electricity; 760 owned cars. Find the cardinalities of
the ultimate sets.
Well guess what? The data is invalid, and he intended it to be. You are supposed to use ultimate sets to make the determination that the data is invalid.....yet it gives NO implication that this is what you are supposed to do.

You would think he would word the question as "use ultimate sets to determine if the data is valid or not"

So anyways you are simply supposed to that The information given is invalid.
• Nov 30th 2011, 04:32 PM
Plato
Re: Cardinalities and ultimate sets
Quote:

Originally Posted by ehpoc
The ultimate sets would be the intersections
AB^c
A^cB
A^cB^c
AB

so for three sets A B C it would be the intersections....
A^cBC
AB^cC
ABC^c
A^cB^cC
A^cBC^c
AB^cC^c
A^cB^cC^c
ABC

What a very odd name for this concept.
I feel for you with this particular instructor. As an ex-dept-chair I know what needs to be done here. If I were you, I would discuss this with your department leader or the Dean of your division.
• Nov 30th 2011, 04:39 PM
ehpoc
Re: Cardinalities and ultimate sets
And say what?
• Nov 30th 2011, 05:01 PM
Plato
Re: Cardinalities and ultimate sets
Quote:

Originally Posted by ehpoc
And say what?

"Why are we being given material so far out of the main stream, the generally accepted, definitions in the area of general set theory". Some stellar professors such as R L Moore can be given a pass on this. But generally I would expect instructors to adhere to standard definitions.
• Nov 30th 2011, 05:22 PM
jar
Re: Cardinalities and ultimate sets
Quote:

Originally Posted by Annatala
Thanks, let us know. Something's definitely fishy...

Oh, and while you're at it, ask him what a positive set and an ultimate set are, since I still have no clue what those mean. (And where did he get those terms...?)

See the below link for positive set.
http://www.mathhelpforum.com/math-he...tml#post698677

Ultimate set is the intersection of all n sets, each is either one of A, B, C,.... or its complement.

These are the definitions given to us in class.

I am hoping he will going to curve the final grade...... (Doh)
• Nov 30th 2011, 06:38 PM
Plato
Re: Cardinalities and ultimate sets
Quote:

Originally Posted by jar
I am hoping he will going to curve the final grade.

I would hope he would be dismissed for gross ignorance.
• Dec 1st 2011, 07:18 AM
Annatala
Re: Cardinalities and ultimate sets
So...here's what I'm gathering from this, parsed into language I can understand:

"Ultimate set" = set
"Positive set" = any set, except for two: U, and U \ (union of all other named sets).
Instructor = stupid, stupid, stupid
Show 40 post(s) from this thread on one page
Page 2 of 2 First 12