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.
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.
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.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.
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.
"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.
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......
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