When the prof was lecturing on cardinality of sets, and ultimate sets, everything seemed quite straightforward. So when I saw this question I thought "No problem"

To my dismay I am completely vexed by it.

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.

A=mortage

B=Car

C=electricity

I am just going to represent not with a ! sign and all sets are intersect.

So the ultimate sets are..

!A !B !C=

A !B !C=

!A B !C=

!A !B C=

A B !C=

A !B C=

!A B C=

A B C=

"570 owned their cottages with no mortgage and also owned cars"

To me this means no mortgage and car which is !A C=570

" 340 owned mortgaged cottages, owned cars, and had electricity"

this is the intersection of |ABC| which is an ultimate set.

"189 had neither mortgages nor cars nor electricity;"

this is an ultimate set |!A!B!C|=189

"760 owned cars"

This is simply |B|=760

So we have

|B|=760

|!A!B!C|=189

|ABC|=340

|U|=1000

|!AC|=570

First does this seem like the correct interpretation? Now I just keep trying to make conclusions from this information, but keep getting lost.