# Thread: need an example here

1. ## need an example here

Let A and B be closed subsets of M, and supposed that both $A \bigcup B$ and $A \bigcap B$ are connected. Prove that A and B are connected.

Find an example of disconnected subsets A,B of R such that $A \bigcup B$and $A \bigcap B$ are connected.

2. ## Re: need an example here

Originally Posted by wopashui
Let A and B be closed subsets of M, and supposed that both $A \bigcup B$ and $A \bigcap B$ are connected. Prove that A and B are connected.

Find an example of disconnected subsets A,B of R such that $A \bigcup B$and $A \bigcap B$ are connected.
Ok, I helped you with the other two. What are your ideas for this one?

3. ## Re: need an example here

Originally Posted by Drexel28
Ok, I helped you with the other two. What are your ideas for this one?
sorry, I have proved the statement, but i'm stuck with the example part, need help on it

4. ## Re: need an example here

Originally Posted by wopashui
sorry, I have proved the statement, but i'm stuck with the example part, need help on it
$\begin{gathered} A = (1,2) \cup (3,4) \hfill \\ B = (0,3] \cup [4,6] \hfill \\ \end{gathered}$

5. ## Re: need an example here

Originally Posted by Plato
$\begin{gathered} A = (1,2) \cup (3,4) \hfill \\ B = (0,3] \cup [4,6] \hfill \\ \end{gathered}$
thanks, in this example, AUB= (0,6) which is connected, and A intersect B= empty set which is connected, and A is disconnected. But is B disconnected? what is the disconnection might be?

6. ## Re: need an example here

Originally Posted by wopashui
thanks, in this example, AUB= (1,7) which is connected, and A intersect B= empty set which is connected, and A is disconnected. But is B disconnected? what is the disconnection might be?
ok