Question

an example of two disconnected sets A, B whose union and intersection are connected

Answer 1

and they have to be in R no less!

Answer 2

\[A=[0,1)\cup(1,3)\]
\[B=[1,2]\cup[3,4]\]

Answer 3

that work?

Answer 4

ok let me think...

Answer 5

they are certainly disconnected

Answer 6

intersection is (1,2]

Answer 7

union is [0,4] looks good to me

Answer 8

that's what I think ;)

Answer 9

many thanks. i had a dumb idea that "disconnected" meant the sets were "disjoint" but that was silly

Answer 10

ah...that would make it hard to do :)

Answer 11

impossible i would say. thanks again

Answer 12

yes