1. real analysis connected sets

Show that it is not necessarily true that if two connected sets have a non-empty intersection, then their intersection will be connected. (a picture will do)

not sure what this would be... any ideas?

2. $\begin{gathered}
A = \left\{ {\left( {x,y} \right) \in \mathbb{R}^2 :y = \sqrt {1 - x^2 } ,-1 \leqslant x \leqslant 1} \right\} \hfill \\
B = \left\{ {\left( {x,y} \right) \in \mathbb{R}^2 :y = - \sqrt {1 - x^2 } ,-1 \leqslant x \leqslant 1} \right\} \hfill \\
\end{gathered}$

3. what does it mean that the intersection is connected?

4. Originally Posted by CarmineCortez
what does it mean that the intersection is connected?
What is the intersection of those two arcs?