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